Researchers Database

YANAGISAWA Taku

FacultyFaculty Division of Natural Sciences Research Group of Mathematics
PositionProfessor
Last Updated :2022/10/06

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Profile and Settings

  • Name (Japanese)

    Yanagisawa
  • Name (Kana)

    Taku

Degree

  • Doctor(Science), Hokkaido University

Research Interests

  • Nonlinear partial differential equations

Research Areas

  • Natural sciences, Basic analysis

Research Experience

  • Dec. 2010, Professor, Faculty of Science, Nara Women's University
  • Apr. 2007, Nov. 2010, Associate Professor, Graduate School of Humanities and SAciences, Nara Women's University
  • Apr. 2003, Mar. 2007, Associate Professor, Graduate School of Humanities and Sciences, Nara Women's University
  • Apr. 1994, Mar. 2003, Associate Professor, Faculty of Science, Nara Women's University
  • Jul. 1991, Mar. 1994, Lecturer, Faculty of Science, Nara Women's University
  • Oct. 1986, Jun. 1991, Assistant Professor, Fuculty of Science, Nara Women's University

Education

  • Apr. 1985, Oct. 1986, Doctor Course of Hokkaido University, Graduate School, Division of Natural Science, Mathemtics
  • Apr. 1983, Mar. 1985, Hokkaido University, 理学研究科博士前期課程, 数学専攻
  • Apr. 1979, Mar. 1983, Hokkaido University, Faculty of Science, Department of Mathematics

Teaching Experience

  • 現象構造解析特論Ⅰ, Nara Women's University
  • Analysis I, Nara Women's University

Association Memberships

  • 日本数学会
  • Japan Mathematical Sociaty

Ⅱ.研究活動実績

Published Papers

  • Refereed, The Journal of Geometric Analysis, Springer Science and Business Media LLC, The Helmholtz–Weyl decomposition of $$L^r$$ vector fields for two dimensional exterior domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, May 2021, 31, 5, 5146, 5165, Scientific journal
  • Refereed, The Journal of Geometric Analysis, Springer Science and Business Media LLC, A Characterization of Harmonic $$L^r$$-Vector Fields in Two-Dimensional Exterior Domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, Dec. 2020, 30, 4, 3742, 3759, Scientific journal
  • Refereed, MANUSCRIPTA MATHEMATICA, SPRINGER, Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems, Hideo Kozono; Taku Yanagisawa, We generalize the well-known Lax-Milgram theorem on the Hilbert space to that on the Banach space. Suppose that a(., .) is a continuous bilinear form on the product X x Y of Banach spaces X and Y, where Y is reflexive. If null spaces N-X and N-Y associated with a(., .) have complements in X and in Y, respectively, and if a(., .) satisfies certain variational inequalities both in X and in Y, then for every F is an element of N-Y(perpendicular to), i.e., F is an element of Y* with F(phi) = 0 for all phi is an element of N-Y, there exists at least one u is an element of X such that a(u,phi) = F(phi) holds for all phi is an element of Y with parallel to u parallel to(X) <= C parallel to F parallel to(Y)*. We apply our result to several existence theorems of L-r-solutions to the elliptic system of boundary value problems appearing in the fluid mechanics., Jul. 2013, 141, 3-4, 637, 662, Scientific journal
  • Refereed, Archive for Rational Mechanics and Analysis, Global Compensated Compactness Theorem for General Differential Operators of First Order, Hideo Kozono; Taku Yanagisawa, Let A1(x, D) and A2(x, D) be differential operators of the first order acting on l-vector functions u = (u1, . . . , u1) in a bounded domain Ω ⊂ ℝn with the smooth boundary ∂Ω. We assume that the H1-norm, is equivalent to, where Bi = Bi(x, ν) is the trace operator onto ∂ Ω associated with Ai(x, D) for i = 1, 2 which is determined by the Stokes integral formula (ν: unit outer normal to ∂Ω. Furthermore, we impose on A1 and A2 a cancellation property such as A1A2′ = 0 and A2A1′ = 0, where Ai′ is the formal adjoint differential operator of Ai(i = 1, 2). Suppose that and converge to u and v weakly in L2(Ω), respectively. Assume also that and are bounded in L2(Ω). If either or is bounded in H1/2(∂Ω), then it holds that. We also discuss a corresponding result on compact Riemannian manifolds with boundary. © 2012 Springer-Verlag Berlin Heidelberg., 2013, 207, 3, 879, 905, Scientific journal
  • Refereed, Lectures on Analysis of Nonlinear Partial Differential Equations: Part 3, \nMorningside Lectures in Mathematics, International Press, L^r Helmholtz Decomposition and Its Application to the Navier-Stokes Equations, Hideo Kozono; Yanagisawa Taku, edited by Fanghua Lin and Ping Zhang, 2013, 3, 237-290, Scientific journal
  • Refereed, MATHEMATISCHE ANNALEN, SPRINGER, Leray's inequality in general multi-connected domains in R-n, Reinhard Farwig; Hideo Kozono; Taku Yanagisawa, Consider the stationary Navier-Stokes equations in a bounded domain whose boundary consists of L + 1 smooth (n - 1)-dimensional closed hypersurfaces I"(0), I"(1), . . . , I" (L) , where I"(1), . . . , I" (L) lie inside of I"(0) and outside of one another. The Leray inequality of the given boundary data beta on plays an important role for the existence of solutions. It is known that if the flux on I" (i) (nu: the unit outer normal to I" (i) ) is zero for each i = 0, 1, . . . , L, then the Leray inequality holds. We prove that if there exists a sphere S in Omega separating in such a way that I"(1), . . . , I" (k) (1 a parts per thousand broken vertical bar k a parts per thousand broken vertical bar L) are contained inside of S and that the others I" (k+1), . . . , I" (L) are outside of S, then the Leray inequality necessarily implies that gamma (1) + center dot center dot center dot + gamma (k) = 0. In particular, suppose that there are L spheres S (1), . . . , S (L) in Omega lying outside of one another such that I" (i) lies inside of S (i) for all i = 1, . . . , L. Then the Leray inequality holds if and only if gamma (0) = gamma (1) = center dot center dot center dot = gamma (L) = 0., Sep. 2012, 354, 1, 137, 145, Scientific journal
  • Refereed, GAKUTO Internat. Ser. Math. Sci. Appl., Analyticity for higher order nonlinear dispersive equations, N. Hayashi; K. Tomoeda; Taku Yanagisawa, 2010, 32, 111-130, Scientific journal
  • Refereed, RIMS Kokyuroku Bessatsu B14, Global DIV-CURL Lemma in 3D bounded domains, Hideo Kozono; Taku Yanagisawa, Nov. 2009, 14, 27-33, Symposium
  • Refereed, PACIFIC JOURNAL OF MATHEMATICS, PACIFIC JOURNAL MATHEMATICS, NONHOMOGENEOUS BOUNDARY VALUE PROBLEMS FOR STATIONARY NAVIER-STOKES EQUATIONS IN A MULTIPLY CONNECTED BOUNDED DOMAIN, Hideo Kozono; Taku Yanagisawa, We consider the stationary Navier-Stokes equations on a multiply connected bounded domain Omega in R(n) for n = 2, 3 under nonhomogeneous boundary conditions. We present a new sufficient condition for the existence of weak solutions. This condition is a variational estimate described in terms of the harmonic part of solenoidal extensions of the given boundary data; we prove it by using the Helmholtz-Weyl decomposition of vector fields over Omega satisfying adequate boundary conditions. We also study the validity of Leray's inequality for various assumptions about the symmetry of Omega., Nov. 2009, 243, 1, 127, 150, Scientific journal
  • Refereed, JOURNAL OF FUNCTIONAL ANALYSIS, ACADEMIC PRESS INC ELSEVIER SCIENCE, Global Div-Curl lemma on bounded domains in R-3, Hideo Kozono; Taku Yanagisawa, We consider a global version of the Div-Curl lemma for vector fields in a bounded domain Omega subset of R-3 with the smooth boundary partial derivative Omega. Suppose that {u(j)}(j=1)(infinity) and {upsilon(j)}(j=1)(infinity) converge to u and upsilon weakly in L-r(Q) and L-r'(Omega), respectively. where 1 < r < infinity with 1/r + 1/r' = 1. Assume also that {div u(j)}(j=1)(infinity) is bounded in L-q (Omega) for q > max{1, 3r/(3+ r)} and that {rot v(j)}(j=1)(infinity) is bounded in L-s(Omega) for s > max {1,3r'/(3 + r')}, respectively. If either {u(j) center dot v vertical bar partial derivative Omega}(j=1)(infinity) is bounded in W-1-1/q,W-q(partial derivative Omega), or {v(j) x v)vertical bar(a Omega)}(j=1)(infinity) is bounded in W-(1-1)/(S.S) (partial derivative Omega) (v: unit outward nomal to partial derivative Omega), then it holds that integral(u)(Omega)(j) dx -> integral(Omega) u . vdx. In particular, if either u(j) .v = 0 or v(j) x v = 0 on partial derivative Omega for all j = 1, 2.... is satisfied, then we have that integral(Omega)uj . v(j) dx -> integral Omega u . vdx. As an immediate consequence. we prove the well-known Div-Curl lemma for any open set in R-3. The Hemholtz-Weyl decomposition tor L-r (Omega) plays an essential role for the proof. (C) 2009 Elsevier Inc. All rights reserved., Jun. 2009, 256, 11, 3847, 3859, Scientific journal
  • Refereed, MATHEMATISCHE ZEITSCHRIFT, SPRINGER, Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data, Hideo Kozono; Taku Yanagisawa, Consider the stationary Navier-Stokes equations in a bounded domain whose boundary consists of multi-connected components. We investigate the solvability under the general flux condition which implies that the total sum of the flux of the given data on each component of the boundary is equal to zero. Based on our Helmholtz-Weyl decomposition, we prove existence of solutions if the harmonic part of the solenoidal extension of the given boundary data is sufficiently small in L(3) compared with the viscosity constant., May 2009, 262, 1, 27, 39, Scientific journal
  • Refereed, INDIANA UNIVERSITY MATHEMATICS JOURNAL, INDIANA UNIV MATH JOURNAL, L-r-variational Inequality for Vector Fields and the Helmholtz-Weyl Decomposition in Bounded Domains, Hideo Kozono; Taku Yanagisawa, We show that every L-r-vector field on Omega can be uniquely decomposed into two spaces with scalar and vector potentials, and the harmonic vector space via operators rot and div, where Omega is a bounded domain in R-3 with the smooth boundary partial derivative Omega. Our decomposition consists of two kinds of boundary conditions such as u . v|(partial derivative Omega) = 0 and u x v |(partial derivative Omega) = 0, where v denotes the unit outward normal to partial derivative Omega. Our results may be regarded as an extension of the well-known de Rham-Hodge-Kodaira decomposition of C-infinity-forms on compact Riemannian manifolds into L-r-vector fields on Omega. As an application, the generalized Blot-Savart law for the incompressible fluids in Omega is obtained. Furthermore, various bounds of u in L-r for higher derivatives are given by means of rot u and div u., 2009, 58, 4, 1853, 1920, Scientific journal
  • Refereed, OSAKA JOURNAL OF MATHEMATICS, OSAKA JOURNAL OF MATHEMATICS, Asymptotic behavior of solutions to the viscous Burgers equation, Taku Yanagisawa, We study the asymptotic behavior of solutions to the viscous Burgers equation by presenting a new asymptotic approximate solution. This approximate solution, called a diffusion wave approximate solution to the viscous Burgers equation of k-th order, is expanded in terms of the initial moments up to k-th order. Moreover, the spatial and time shifts are introduced into the leading order term to capture precisely the effect of the initial data on the long-time behavior of the actual solution. We also show the optimal convergence order in L-p-norm, 1 <= p <= infinity, of the diffusion wave approximate solution of k-th order. These results allow us to obtain the convergence of any higher order in L-p-norm by taking such a diffusion wave approximate solution with order k large enough., Mar. 2007, 44, 1, 99, 119, Scientific journal
  • Not Refereed, 数理解析研究所講究録, Hodge decomposition of L^r-vector fields on a bounded domain and its application to the Navier-Stokes equations, Taku Yanagisawa, 2007, 1536, 73-86
  • Refereed, COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, JOHN WILEY & SONS INC, Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane, ZP Xin; T Yanagisawa, The zero-viscosity limit for an initial boundary value problem of the linearized Navier-Stokes equations of a compressible viscous fluid in the half-plane is studied. By means of the asymptotic analysis with multiple scales, we first construct an approximate solution of the linearized problem of the Navier-Stokes equations as the combination of inner and boundary expansions. Next, by carefully using the technique on energy methods, we show the pointwise estimates of the error term of the approximate solution, which readily yield the uniform stability result for the linearized Navier-Stokes solution in the zero-viscosity limit. (C) 1999 John Wiley & Sons, Inc., Apr. 1999, 52, 4, 479, 541, Scientific journal
  • Refereed, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, The initial boundary value problem for linear symmetric hyperbolic systems with boundary characteristic of constant multiplicity, M Ohno; Y Shizuta; T Yanagisawa, Jul. 1995, 35, 2, 143, 210, Scientific journal
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, NOTE ON GLOBAL EXISTENCE FOR AXIALLY-SYMMETRICAL SOLUTIONS OF THE EULER SYSTEM, T SHIROTA; T YANAGISAWA, Dec. 1994, 70, 10, 299, 304, Scientific journal
  • Refereed, TOHOKU MATHEMATICAL JOURNAL, TOHOKU UNIVERSITY MATHEMATICAL INSTITUTE, THE TRACE THEOREM ON ANISOTROPIC SOBOLEV SPACES, M OHNO; Y SHIZUTA; T YANAGISAWA, The trace theorem on anisotropic Sobolev spaces is proved. These function spaces which can be regarded as weighted Sobolev spaces are particularly important when we discuss the regularity of solutions of the characteristics initialo boundary value problem for linear symmetric hyperbolic systems., Sep. 1994, 46, 3, 393, 401, Scientific journal
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, A CONTINUATION PRINCIPLE FOR THE 3-D EULER EQUATIONS FOR INCOMPRESSIBLE FLUIDS IN A BOUNDED DOMAIN, T SHIROTA; T YANAGISAWA, Mar. 1993, 69, 3, 77, 82, Scientific journal
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, THE INITIAL BOUNDARY-VALUE-PROBLEMS FOR LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS WITH CHARACTERISTIC BOUNDARY, M OHNO; Y SHIZUTA; T YANAGISAWA, Jun. 1991, 67, 6, 191, 196, Scientific journal
  • Refereed, COMMUNICATIONS IN MATHEMATICAL PHYSICS, SPRINGER VERLAG, THE FIXED BOUNDARY-VALUE-PROBLEMS FOR THE EQUATIONS OF IDEAL MAGNETO-HYDRODYNAMICS WITH A PERFECTLY CONDUCTING WALL CONDITION, T YANAGISAWA; A MATSUMURA, The equations of ideal Magneto-Hydrodynamics are investigated concerning initial boundary value problems with a perfectly conducting wall condition. The local in time solution is proved to exist uniquely, provided that the normal component of the initial magnetic field vanishes everywhere or nowhere on the boundary., 1991, 136, 1, 119, 140, Scientific journal
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, INITIAL BOUNDARY-VALUE PROBLEM FOR THE EQUATIONS OF IDEAL MAGNETO-HYDRO-DYNAMICS WITH PERFECTLY CONDUCTING WALL CONDITION, T YANAGISAWA; A MATSUMURA, Jun. 1988, 64, 6, 191, 194, Scientific journal
  • Refereed, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, JAPAN ACAD, MIXED PROBLEMS FOR QUASI-LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS, S KAWASHIMA; T YANAGISAWA; Y SHIZUTA, Sep. 1987, 63, 7, 243, 246, Scientific journal
  • Refereed, Hokkaido Mathematical Journal, The initial boundary value problem for the equations of ideal magneto-hydrodynamics, Taku Yanagisawa, 1987, 16, 3, 295, 314, Scientific journal
  • Refereed, Journal of Functional Analysis, Elsevier BV, L^r-Helmholtz-Weyl decomposition for three dimensional exterior domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, Oct. 2021, 281, 8, 109144, 109144, Scientific journal
  • Refereed, Calculus of Variations and Partial Differential Equations, Springer Science and Business Media LLC, Stationary Navier–Stokes equations under inhomogeneous boundary conditions in 3D exterior domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, Jul. 2021, 60, 5, Scientific journal
  • Refereed, The Journal of Geometric Analysis, A Characterization of Harmonic L^r-Vector Fields in Three Dimensional Exterior Domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, 19 May 2022, 32, Scientific journal

MISC

  • Not Refereed, 数理解析研究所講究録, Boudary Value Problems for Stationary MHD Equations, YANAGISAWA Taku, Jul. 2014, 1905, 40-52
  • Not Refereed, 研究集会PPM2010報告集 \n偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2010, 多重連結領域における定常Navier-Stokes方程式の境界値問題, YANAGISAWA Taku, 2011, PPM2010-10, 1-9
  • Not Refereed, 日本数学会2010年度年会函数方程式論分科会講演アブストラクト, Helmholtz-Weyl分解とその応用, YANAGISAWA Taku, Mar. 2010, 122-131
  • Not Refereed, 数理解析研究所講究録, On the paper "Blows Ups of Complex Solutions of the 3D Navier-Stokes Systems and RG Method" by Ya Sinai and et al., YANAGISAWA Taku, 2008, 1600, 132-146
  • Not Refereed, 数理解析研究所講究録, 理想磁気流体力学の方程式系の初期値境界値問題, YANAGISAWA Taku, 1990, 734, 91-105

Books etc

  • Advances in Nonlinear Partial Differential Equations and Stochastics (Series on Advances in Mathematics for Applied Sciences Vol.48), World Scientific, YANAGISAWA Taku; S. Kawashima, 編集, Jan. 1998, Not Refereed

Presentations

  • Taku Yanagisawa, Maximal regularity and nonlinear (RIMS, Kyoto), On the spaces of harmonic L^r-vector fields over exterior domains, Mar. 2019, RIMS, Kyoto University, Kyoto, Japan, True
  • Taku Yanagisawa, Mathematical Fluid Mechanics and Related Topics -In honor of Professor Hideo Kozono on his 60th birthday-(Tokyo Institute of Technology, Tokyo), A geometric characterization of the space of harmonic L^r-vector fields over exterior domains, Sep. 2018, Yasuhi Taniuchi et.al., Tokyo Institute of Technology, Ookayama Campus, True
  • YANAGISAWA Taku, ミニシンポジュウム(北海道情報大学), Arithmetic-Geometric mean and Newton's method, Sep. 2018, 北海道江別市 北海道情報大学EDタワー, False
  • Taku Yanagisawa, The 35th Kyushu Symposium on Partial Differential Equations, Characterization of the space of harmonic vector fields over exterior domains, Jan. 2018, Shuichi Kawashima, Yoshiyuki Kagei, et.al., Nishijin Plaza, Kyushu University, True
  • Taku Yanagisawa, 第6回岐阜数理科学研究会, 外部領域上の調和ベクトルのなす空間について, Aug. 2017, 岐阜大学サテライトキャンパス 多目的講義室, False
  • YANAGISAWA Taku; Taku Yanagisawa, The Navier-Stokes Equations and Related Topics -In Honor of the 60th Birthday of Professor Reinhard Farwig-(Nagoya University, Nagoya), On the existence and stability of stationary solutions of MHD equations under the inhomogeneous boundary conditions, Mar. 2016, Nagoya University, Nagoya, True
  • YANAGISAWA Taku; Taku Yanagisawa, RIMS Workshop on Mathematical Analysis in Fluid and Gasdynamics, On the stability of stationary solutions to the MHD equations with large boundary data, Jul. 2015, RIMS, Kyoto University, Kyoto, True
  • YANAGISAWA Taku, 第4回弘前非線形方程式研究会, The solvability and stability of boundary value problems for stationary MHD equations, Dec. 2014, 堤誉志雄,伊藤成治,津田谷公利,山本征法,岡部考宏, 弘前大学創立50周年記念会館「岩木ホール」, False
  • YANAGISAWA Taku; Taku Yanagisawa, Classical Problems and New Trends in Mathematical Fluid Dynamics on occasion of Professor Konstantin Pileckas' 60th birthday, The boundary value problem for stationary MHD equations, Oct. 2014, Amann, Galdi, Rautmann, Solonnikov 他, Ferrara, Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, ICM 2014 Satellite Conference, Mathematical Theory of Gases and Fluids and Related Applications, The solvability and stability of boundary value problems for stationary MHD equations, Aug. 2014, Donho Chae, Tai-Ping Liu, Hisashi Okamoto, Chung-Ang University, Seoul, Korea, True
  • YANAGISAWA Taku; Taku Yanagisawa, Fluid Dynamics and Electromagnetism: Theory and Numerical Approximation on occasion of Prof. Paolo Secchi and Alberto Valli 60th birthday, The stability of stationary solutions to the MHD equations under the inhomogeneous boundary condition, Jun. 2014, L. Berselli et. al., Levico Terme, Trento, Italy, True
  • YANAGISAWA Taku, 大阪市大・大阪府大合同「第19回南大阪応用数学セミナー」, 定常MHD方程式に対する非斉次境界値問題について, Jun. 2014, 高橋太,壁谷喜継 他, 大阪府立大学中百舌鳥キャンパス数理工学科B9棟111号室, False
  • YANAGISAWA Taku; Taku Yanagisawa, Recent Advances in PDEs and Applications on occasion of Professor Hugo Beirao da Veiga's 70th birthday, Solvability of boundary value problems of the stationary MHD systems, Feb. 2014, V. A. Solonnikov, P. Secchi 他, Levico Terme, Trento, Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, Mathematical Analysis of Nonlinear Partial Differential Equations -In honor of Professor Shuichi Kawashima on his sixtieth birthday-, On the solvability of boundary value problems for the stationary MHD equations with inhomogeneous boundary conditions, Nov. 2013, Yoshiyuki Kagei et.al, Kyushu University Nishijin Plaza, Japan, True
  • YANAGISAWA Taku; Taku Yanagisawa, Mathematical Analysis of Viscous Incompressible Fluid, RIMS Symposium, Boundary value problems for stationary MHD equations, Nov. 2013, 菱田俊明、柴田良弘、清水扇丈, 京都大学数理解析研究所, True
  • YANAGISAWA Taku; Taku Yanagisawa, Nonlinear Wave Equation and Fluid Mechanics\n-In honor of Professor Thomas C. Sideris on his sixtieth birthday-, On the solvability Navier-Stokes equations with nonhomogeneous boundary condition, Aug. 2013, Ogawa Takayoshi et.al., Muroran Institute of Technology, Muroran, Japan, True
  • YANAGISAWA Taku, 語ろう数理解析, 非斉次境界条件下での定常Navier-Stokes方程式の境界値問題をめぐって, Jan. 2012, 名和,石渡,松本他, 京都大学理学部, False
  • YANAGISAWA Taku; Taku Yanagisawa, Partial Differential Equations in Mathematical Physics and their Numerical Approximation, Boundary value problems of the stationary MHD equations and Navier-Stokes equations with Coriolis force, Sep. 2011, Hugo Beirao da Veiga, A, Valli, Levico Terme (Trento), Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, The 4th MSJ-SI: Nonlinear Dynamics in Partial Differential Equations, Applications of Hodge decomposition to mathematical fluid dynamics, Sep. 2011, 日本数学会, 川島秀一他, Kyushu Univ. Hakata, Japan, False
  • YANAGISAWA Taku; Taku Yanagisawa, International Conference on Fluid and Gas Dynamics, On global compensated compactness theorem, Sep. 2011, Yong Zhou, Wuxing Hotel, Jinhua, China, True
  • YANAGISAWA Taku; Taku Yanagisawa, 7th Internatinal Congress on Industrial and Applied Mathematics, Minisimposium "Recent topics on mathematical analysis for the Navier-Stokes equations", On the stationary boundary value problems of the Navier-Stokes equations with in and out flow on the boundary, Jul. 2011, Shin'ya Matsui and Yoshikazu Giga, Vancouver, BC, Canada, True
  • YANAGISAWA Taku; Taku Yanagisawa, International Conference on Mathematical Fluid Mechanics and Biomedical Applications, The solvability of stationary Navier-Stokes equations with inhomogeneous boundary data, Jun. 2011, G.Galdi, Hugo Beirao da Veiga, A. Robertson他, Ponta Delgada, Azores, Portugal, True
  • YANAGISAWA Taku; Taku Yanagisawa, International Workshop on Interaction between Mathematics and Fluid Mechanics, The stationary Navier-Stokes equations under the inhomogeneous boundary conditions, Mar. 2011, 鈴木貴,河原源太, 大阪大学基礎工学部, False
  • YANAGISAWA Taku; Taku Yanagisawa, The 3rd Nagoya Workshop on Differential Equations, On global compensated compactness theorem, Feb. 2011, 杉本充,菱田俊明, 名古屋大学理1号館, False
  • YANAGISAWA Taku; Taku Yanagisawa, PDE and Mathematical Physics, Global compensated compactness theorem and its applications, Nov. 2010, 千原浩之他, 京都大学芝蘭会館別館, False
  • YANAGISAWA Taku, 偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2010, 多重連結領域における定常Navier-Stokes方程式の境界値問題, Nov. 2010, 辻川他, 宮崎大学工学部, False
  • YANAGISAWA Taku, PDE白田記念会ミニシンポジウム, 熱方程式とモーメント問題, Aug. 2010, 佐藤剛, 北海道大学大学院理学研究科, False
  • YANAGISAWA Taku, 青葉山勉強会(第5回), 調和ベクトル場と流体力学等に現れる定常解, Jun. 2010, 久保英夫, 東北大学情報科学研究科, False
  • YANAGISAWA Taku, 乱流場と非線形構造-数学と流体力学の融合を目指して-, ベクトル場の分解定理とその流体力学への応用, Apr. 2010, 金田行雄,小薗英雄,石原卓, 東北大学 数理科学記念館, False
  • YANAGISAWA Taku, 日本数学会2010年度年会函数方程式論分科会特別講演, Helmholtz-Weyl分解とその応用, Mar. 2010, 日本数学会, 慶応義塾大学, False
  • YANAGISAWA Taku; Taku Yanagisawa, Linear and Nonlinear Waves, No.7, Asymptotic behavior of solutions to the viscous Burgers equation, Nov. 2009, T.Nishitani, N.Hayashi, and H.Sunagawa, 大津市, False
  • YANAGISAWA Taku, 第2回CESセミナー, 境界層方程式について, Nov. 2009, 笹山,松井, 早稲田大学理工学部, False
  • YANAGISAWA Taku; Taku Yanagisawa, Conference on "Mathematical Physics and PDEs", On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition, Sep. 2009, Hugo Beirao da Veiga, Alberto Valli, Levico Terme(Trento, Italy), True
  • YANAGISAWA Taku; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I, May 2009, Yong Zhou, Zhejiang Normal University, Jinhua, China, True
  • YANAGISAWA Taku; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data II, May 2009, Yong Zhou, Zhejiang Normal University, Jinhua, China, True
  • YANAGISAWA Taku; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's inequality in 3D domains, May 2009, Yong Zhou, Zhejiang Normal University, Jinhua, China, True
  • YANAGISAWA Taku; Taku Yanagisawa, Topics of Fluid Dynamics, Blow-up criteria for smooth solutions of 3-D compressible Euler equations on a bounded domain, Apr. 2009, Paolo Secchi, Brescia University, Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, Series of Lectures at Pisa University (Parts I and II), Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I, II, Mar. 2009, Hugo Beirao da Veiga, Pisa University, Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, Series of lectures at Pisa University (Part III), Leray's inequality in 3D domains, Mar. 2009, Hugo Beirao da Veiga, Pisa University, Italy, True
  • YANAGISAWA Taku; Taku Yanagisawa, Series of lectures at Pisa University (Part IV), Global DIV-CURL lemma, Mar. 2009, Hugo Beirao da Veiga, Pisa University, Italy, True
  • YANAGISAWA Taku, 早稲田大学PDEセミナー, Sinai等によるNavier-Stokes方程式に関する研究の紹介, Nov. 2008, 柴田良弘 小澤徹, False
  • YANAGISAWA Taku, Nonlinear PDE Workshop at Sendai, Blow-up criteria of smooth solutions for 3-D compressible Euler equations in a bounded domain, Nov. 2008, 谷内靖,石毛和弘,鈴木友之, 東北大学青葉山キャンパス数理科学記念館, False
  • YANAGISAWA Taku; Taku Yanagisawa, The Banach Center Conference: Parabolic and Navier-Stokes Equations 2008, Helmholtz-Weyl decomposition and its application to compressible Euler flows on a bounded domain, Sep. 2008, H.Amann, Y.Shibata,, Bedlewo, Poland, True
  • YANAGISAWA Taku; Taku Yanagisawa, Workshop on Mathematical Fluid Dynamics, Global DIV-CURL Lemma on bounded domains, Sep. 2008, H.Amann, Darmstadt, Germany, True
  • YANAGISAWA Taku; Taku Yanagisawa, PDE Seminar, Konstanz University, A decomposition theorem of L^r-vector fields over a bounded domain and its application, Sep. 2008, R. Racke, Konstanz University, Konstanz, Germany, True
  • YANAGISAWA Taku; Taku Yanagisawa, Navier-Stokes equations:Classical and generalized models, Leray's problem on the stationary Navier-Stokes equations and Leray's inequality, Sep. 2008, H.Beirao da Veiga, Centro di Recerca Matematica Ennio De Giorgi, Scoula Normale Superiore di Pisa, Pisa, Italy, True
  • YANAGISAWA Taku, 大阪大学水曜セミナー, Global DIV-CURL lemma on bounded domains in \R^3, Jul. 2008, 松村昭孝, 阪大 理学部, False
  • YANAGISAWA Taku, 第2回奈良偏微分方程式研究会, Leary's problem on the stationary Navier-Stokes equations and Leray's inequality, Jun. 2008, 柳沢 卓, 奈良女子大学, False
  • YANAGISAWA Taku; Taku Yanagisawa, PDE Seminar at Fachbereich Mathematik, Technische Universitat Darmstadt, Leray's problem on the stationary Navier-Stokes equations and Leray's inequality, Jun. 2008, Reihard Farwig, Darmstadt, Germany, True
  • YANAGISAWA Taku, 第1回RIMS合宿型セミナー「数理流体力学:抽象論と計算力学的手法の融合」, A Decomposition Theorem and its application to fluid dynamics, Mar. 2008, 岡本久(京大数理解析研), 神戸インスティチュ-ト, False
  • YANAGISAWA Taku, 若手による流体力学の基礎方程式研究集会, Sinai 等によるNavier-Stokes方程式に関する最近の研究の紹介, Jan. 2008, 小薗英雄他, 名古屋大学大学院多元数理科学研究科, False
  • YANAGISAWA Taku, RIMS研究集会「繰りこみ群の数理科学での応用」, On the paper "Blow Ups of Complex Solutions of the 3D Navier-Stokes System and RG Method" by Ya Sinai et al., Sep. 2007, 伊東 恵一(摂南大学・工学部), 京都大学数理解析研究所, False
  • YANAGISAWA Taku; Taku Yanagisawa, Sapporo PDE Symposium, Leray's problem for the stationary Navier-Stokes equations and the harmonic vector fields II, Aug. 2007, T.Ozawa, Hokkaido Univ., True
  • YANAGISAWA Taku; Taku Yanagisawa, Second Workshop on Nonlinear Partial Differential Equations: Analysis, Computation and Application, Decomposition theorems of vector fields and the application to the Navier-Stokes equations, Jun. 2007, Seung Yeal Ha, Yong Jung Kim, Seoul National University, Korea, True
  • YANAGISAWA Taku, 神戸大学解析セミナー, On flux problems for the stationary Navier-Stokes equation, Jun. 2007, 足立、高岡, 神戸大学, False
  • YANAGISAWA Taku, 非線形解析セミナー, The flux problem for stationary Navier-Stokes eqautions in a bounded domain with a mutiply connected boundary, May 2007, 谷 温之, 慶応大学, False
  • YANAGISAWA Taku, Nonlinear PDE seminar (Osaka University), Existence of solutions of nonhomogeneous boundary value problem for stationary Navier-Stokes equations in a bounded domain Nonlinear PDE seminar (Osaka University), Dec. 2006, 松村 昭孝, False
  • YANAGISAWA Taku, 第2回 流体と保存則の研究集会, Nonhomogeneous boundary value problems for the stationary Navier Stokes equations in a multiply connected domain, Oct. 2006, 西畑 伸也, 東京 (東京工業大学), False
  • YANAGISAWA Taku, 北海道情報大学偏微分方程式セミナー, 粘性Burgers方程式の解の長時間漸近挙動, Sep. 2006, 松井 伸也, 札幌 (北海道情報大学), False
  • YANAGISAWA Taku; Taku Yanagisawa, Mathematical Analysis in Fluid and Gas Dynamics, Hodge decomposition of L^r vector fields on a bounded domain and its application to the Navier Stokes equations, Jul. 2006, Y.Kagei, RIMS, Kyoto, Japan, True
  • YANAGISAWA Taku, Nolinear PDE seminar (Osaka University), Asymptotic behavior of solutions to the viscous Burgers equation, May 2006, 松村 昭孝, 大阪大学, False
  • YANAGISAWA Taku, 第3回非線形偏微分方程式研究集会, 有界領域上の調和形式の構成とHodge分解定理, Mar. 2006, 三沢 正史、菱田 俊明, 富山県氷見市, False
  • YANAGISAWA Taku; Taku Yanagisawa, 2006 Korea-Japan Conference on Partial Differential Equations, On the decomposition theorem of L^r-vector fields on a bounded domain, Mar. 2006, HI Jun Choe, Hideo Kozono, Yonsei University, Seoul, Korea, True
  • YANAGISAWA Taku, 解析学談話会(函館みらい大学), ベクトル場の分解定理に関連する幾つかの不等式について, Feb. 2006, 上見練太朗, 函館, False
  • YANAGISAWA Taku, 北大 PDE Seminar, 有界領域上のベクトル場のHodge分解定理, Nov. 2005, 小澤 徹, 札幌, False
  • YANAGISAWA Taku; Taku Yanagisawa, The Fourth International Conference on Nonlinear Analysis and Convex Analysis, Asymptotic behavior of solutions to the viscous Burgers eqaution with degenerate initial moments, Jul. 2005, W. Takahashi, T. Tanaka, Okinawa, Japan, True

Research Projects

  • Fund for the Promotion of Joint International Research (Fostering Joint International Research (B)), 07 Feb. 2019, 31 Mar. 2023, 18KK0072, Modern Mathematical Analysis for the Fluid Dynamics, 清水 扇丈; 小薗 英雄; 柳沢 卓; 筒井 容平; 高田 了, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Fund for the Promotion of Joint International Research (Fostering Joint International Research (B)), Kyoto University, 17680000, 13600000, 4080000, 小薗-柳沢-清水は, ドイツDarmstadt工科大学のHieber教授とSeyfert博士との国際共同研究で, 2次元外部領域におけるLr-調和ベクトル場, すなわち発散ゼロおよび回転ゼロを満たすベクトル場の次元を決定した. ベクトル場が満たす方程式により, 法線方向が0である境界条件を課した空間Xrと, 接線方向が0である境界条件を課した空間Vrを考察する必要がある. 2次元の場合には, 90度回転させるとXrとVrは等しくなるため次元も等しく, 2より大きく無限未満のrに対しては空洞の個数に等しく, 1より大きく2以下の間のrに対しては空洞の個数-1であることを証明した. 2は2次元のPoisson方程式の斉次Dirichlet境界問題の弱解の可解性の閾値である. 2次元および3次元の外部領域に対するHelmholtz-Weyl型直和分解定理, すなわちLrベクトル場を, その調和部分, ベクトルポテンシャル, スカラーポテンシャルに分解する定理を上記5名の共同研究として導き, 口頭発表を行った. 清水は, イタリアCampania大学のMaremonti教授との国際共同研究で, 3次元外部領域における減衰しない初期値に対する初期値-境界値問題を考察した. 本質的有界, かつコンパクトな台を持つ無限回微分可能な関数空間で発散ゼロの空間を空間1階微分のLp (p>3)ノルムで完備化した空間に属する任意の大きさの初期値に対して, 時間大域的な弱解が存在することを証明した. 筒井は, 局所平滑化作用素に対する疎性上界についての成果を得た. 高田は, Hieber教授とArizona state大学のMahalov教授との国際共同研究で, 回転成層流体に対する3次元粘性 Boussinesq 方程式の時間周期問題を考察し,時間周期解および時間概周期解の存在と一意性を証明した.
  • 奨励研究, 2019, 2019, 19H00131, 幼小一貫した資質・能力を育成する「育ちの履歴カリキュラム」に関わる研究, 松田 登紀; 柳沢 卓; 飯島 貴子; 柿元 みはる; 辻岡 美希; 角田 三友紀; 鎌内 菜穂; 越智 裕子; 福西 まゆみ, 日本学術振興会, 科学研究費助成事業 奨励研究, 奈良女子大学, 470000, 470000, 0, 本研究では、幼小一貫した実践から「育成したい資質・能力」を描き出す3歳~5歳の「育ちの履歴カリキュラム」を編成するにあたり、教師の意図や願いが視覚的に読み取れるようデザイン開発を行うことを目的とした。 カリキュラムをデザインする過程において、以下の成果が見られた。(1)実践者が無自覚であった資質・能力の観点を記録写真に再発見することになり、実践でより資質・能力を意識するきっかけとなる、(2)実践写真を基に他者と対話をすることにより、自らの保育観を自覚することにつながる、(3)写真は公開した時から見る側の経験に理解を委ねる特性をもつ。, url
  • Grant-in-Aid for Scientific Research (C), 01 Apr. 2015, 31 Mar. 2018, 15K04957, Studies on mathematical structure of boundary value problems appearing in hydrodynamics and magnetohydrodynamics, YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 4680000, 3600000, 1080000, This research was intended as an attempt to study the relations, from a mathematical standpoint, between the following three issues on the boundary value problems appearing in the hydrodynamics and magnetohydrodynamics (MHD) : (i) the nonlinear structure of equations, (ii) the setting of boundary conditions, (iii) the geometrical structure of domains. Our results obtained in this reserach can be listed below. (1) We proved the existence and the stability of weak solutions of stationary MHD equations under inhomogeneous boundary conditions.(2) We gave a characterization of harmonic vector fields in three dimensional exterior domain by topological invariants of exterior domains. This result shall be a base for establishing Hodge decomposition theorem for exterior domains., url
  • Grant-in-Aid for Scientific Research (C), 01 Apr. 2012, 31 Mar. 2015, 24540173, The development of the unified analytical method to hydrodynamical and electromagnetic phenomena based on decomposition theorems, YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 4940000, 3800000, 1140000, Applying our analytical method based on decomposition theorems to the stationary boundary value problems of MHD equations, we investigate the effectiveness or the subjects to be examined of our analytical method. In fact, we succeed in proving the existence of the weak solutions with inhomogeneous boundary data. In the process of the proof, we clarify some points which reflect the peculiar mathematical structures of MHD equations. We can also obtain some results suggesting that our analytical method based on decomposition theorems might be effective even in the stability analysis., url
  • Grant-in-Aid for Scientific Research (C), 01 Apr. 2012, 31 Mar. 2015, 24540400, Dynamical feature of mathematically obtained m-point blow-up solution in mean field equation for two-dimensional point vortex system, YATSUYANAGI Yuichi; HATORI Tadatsugu; YANAGISAWA Taku; OHTSUKA Hiroshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Shizuoka University, 5070000, 3900000, 1170000, It is mathematically anticipated by Nagasaki and Suzuki that in the two-dimensional point vortex system there is an equilibrium singular solution diverging at m points whose inverse temperature is given by β = -8πm. Our final goal is to understand the solution dynamically. The following notations are used here: u velocity field, ω vorticity, ψ stream function. The point vortex system relaxes violently by the second term div(uω) in the Euler equation. After the violent relaxation, the system reaches a state characterized by div(uω)=0. In this state there are many small regions with different temperature and in each region, the collisional effect vanishes. The small diffusive effect remains due to the interaction between small regions with different beta. This is the main mechanism of the slow relaxation in the point vortex system., url
  • Grant-in-Aid for Scientific Research (B), 01 Apr. 2011, 31 Mar. 2015, 23340036, Large time behaviors of solutions of nonlinear conservation laws with dissipative structures of energy, MATSUMURA Akitaka; CHAWANYA Takeshi; ODANAKA Shinji; NISHIHARA Kenji; NISHIBATA Shinya; YANAGISAWA Taku; TSUGE Naoki; IOHARA Takao, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Osaka University, 11830000, 9100000, 2730000, Various weighted energy methods were successfully manipulated to have a priori estimates for solutions of nonlinear conservation laws with dissipative structures of energy. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of ideal gas, dissipative wave equations, model system of semiconductor, large scale dynamical system, etc. As for a model system of semiconductor, which is very important in practical applications, an efficient method of numerical computation to get the stationary solutions was proposed., url
  • Grant-in-Aid for Scientific Research (C), 2009, 2011, 21540179, Clarification of the mathematical structure of fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain., YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 3510000, 2700000, 810000, Several phenomena of fluid or electromagnetism seem to have close relation to topological properties of the domain in which the phenomena occur. Here the topological properties of the domain mean, for example, the number of the inner boundary components and the genus of the outer boundary component of the domain. This research discusses new analytical methods based on the decomposition theorem of vector fields on the domain and the singular perturbation, aiming at clarifying the mathematical structure of such fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain., url
  • Grant-in-Aid for Scientific Research (B), 2007, 2010, 19340037, Time global structure of solutions of nonlinear conservation law with viscosity and relaxation, MATSUMURA Akitaka; CHAWANYA Takeshi; ODANAKA Shinji; NISHIHARA Kenji; NISHIBATA Shinya; YANAGISAWA Taku; KOMATSU Gen; TSUGE Naoki; IOHARA Takao, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Osaka University, 11960000, 9200000, 2760000, Several new weighted energy methods were successfully proposed to have a priori estimates of solutions. With the aid of these methods, has been much progressed the analysis on the large time behaviors of the solutions of scalar viscous conservation law with non-convex flux, system of equations of viscous ideal gas, dissipative wave equations, etc. Also for model equations of semiconductor, the analysis on existence, uniqueness and asymptotic stability of stationary solutions, hierarchy structures with respect to several physical parameters, and methods of numerical computation has been much progressed., url;url
  • Grant-in-Aid for Scientific Research (S), 2003, 2007, 15104001, United theory of existence of global solution and its asymptotic behavior to the nonlinear partial differential equations, KOZONO Hideo; TAKAGI Izumi; YANAGIDA Eiji; OGAWA Takayoshi; YANAGISAWA Taku; NAKAMURA Makoto, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S), Tohoku University, 79300000, 61000000, 18300000, 1. Constructions of very weak solutions of the Navier-Stokes equations in exterior domains. We show the unique existence of local very weak solutions to the prescribed non-homogeneous boundary data which belong to the larger class than the usual trace class. Our solutions satisfy the Serrin condition which implies the scaling invariant class. 2. New regularity criterion on weak solutions of the Navier-Stokes equations. We prove that every turbulent solution which is α-Hoelder continuous in the kinetic energy in the time interval with α>1/2 necessarily regular. 3. Helmholtz-Weyl de composition in unbounded domains with non-compact boundaries of uniformly C^2-class. Despite of a counter example of valiclity of the Helmholtz-Weyl decomposition in L^r, we introduce the space of sum and intersection of L^r and prove the Helmholtz-Weyl decomposition in such spaces. As an application, we can define the Stokes operator.
  • Grant-in-Aid for Scientific Research (C), 2001, 2003, 13640173, Boundary value problems for hyperbolic systems from fluid-mechanics and electromagnetics arising as the limit of singular perturbation, YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 1500000, 1500000, For the purpose of building the mathematical framework to investigate the boundary value problems for hyperbolic systems as the limit of singular perturbation, we have shown the following mathematical results through the consideration of concrete problems appearing in the fluid-mechanics. 1)."Vanishing viscosity limit for the initial boundary value problems of the compressible Navier-Stokes equations in a domain with the boundary" We study the existence theorem for the initial boundary value of the Prandtl equation which appears as the first term of the boundary expansion of asymptotic solution to the compressible Navier-Stokes equations. By taking the Fokker-Planck type equation as the linearized equation, we can show the estimate with the improvement in the order of regularity. However, it is also observed that there should occur the phenomenon of the "loss of derivatives" for this linearized problem. Hence it is so far most likely to be difficult to show the existence theorem for the Prandtl equation in the Sobolev spaces. 2)."On the relation of the smoothness of the solutions of the 3-D Navier-Stokes equations in a bounded domain with the vorticity" We have shown a new a-priori estimate of the solutions to the 3-D Navier-Stokes equations in a bounded domain which reveals that the maximum norm of the vorticity controls the smoothness of the solutions. Further we presented a generalized Biot-Savart law on a bounded domain with the estimates of the Green's matrix of the Laplace operator, which was used in the proof of the new a-priori estimate stated above.
  • Grant-in-Aid for Scientific Research (C), 1999, 2001, 11640211, Analysis of singular perturbations of the Navier-Stokes equations, MATSUI Sin'ya; YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Hokkaido Information University, 3700000, 3700000, In this project I researched jointly with Professor Yanagisawa, Professor Giga, Professor Ishimura and others. The papers which we published are stated in References. In these papers we studied the Navier-Stokes equations in the whole space or in the half space and studied zero viscosity limit of the compressible viscous fluid in the half plane. The pre-print papers are the followings : (with Ishimura, N.) On blow-up solutions of the Blasius equation. (with Giga, Y. and Sasayama, T.) Blow up rate for a semilinear heat equation with subcritical nonlinearity.
  • 萌芽的研究, 1999, 2000, 11874028, 特異摂動極限として流体及び電磁気学に現れる双曲系境界値問題, 柳沢 卓, 日本学術振興会, 科学研究費助成事業 萌芽的研究, 奈良女子大学, 2200000, 2200000, 流体力学に現れる準線型対称双曲系の典型例である圧縮性オイラー方程式に対する初期境界値問題を,特異摂動極限として捉えるための枠組みとして,物理的にも自然で重要な問題である,半空間における圧縮性粘性流体の非粘性極限問題を取り上げ、以下の点を明らかにした。 1.以前,線型化問題に対して適用した多重スケール変換を用いた漸近解析法により,圧縮性粘性流体の近似解を内部展開項と境界層展開項の和として求めた。この際,境界層展開において非線型問題として現れてくるのは,質量密度と流体速度の法線成分の第1項目に対する常微分方程式の2点境界値問題と,流体速度の接線成分の第1項目に対するPrandtl方程式の初期境界値問題である。この2つの非線型問題の存在定理を示すことが次の目標となる。しかし,Prandtl方程式の初期境界値問題に対しては接線微分のエネルギー評価を示すことが困難なことから,通常のソボレフ空間での解の存在定理を示すことは難しいと考えていた。しかし,最近,従来Prandtl方程式の線型化を行なうときに低階項と見なしてきた項を主要部に取り入れることにより,線型Fokker-Planck方程式と類似の評価が成り立ち,これを用いれば接線微分の(1未満の)分数階微分の評価は得られることがわかった。今後,この評価により非線型性をどこまでコントロールできるかを検討していきたい。 2.初期値が境界条件との適合条件を満たすことを用いて、上で(形式的に)構成した近似解の境界層展開項の第1項目に対する一様評価を,時間を十分短く限ることにより示すことができた。このことを用いて誤差項の一様評価が得られるかどうか考察を進めたい。
  • Grant-in-Aid for Scientific Research (B), 1997, 1999, 09440061, CHARACTERISTIC BOUNDARY VALUE PROBLEM FOR LINEAR AND NONLINEAR SYMMETRIC HYPERBOLIC SYSTEMS, SHIZUTA Yasushi; YAMAMOTO Mayumi; TOMOEDA Kenji; KASAHARA Kouji; SHINODA Masato; YANAGISAWA Taku, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), 6900000, 6900000, (1) We obtained a final form of the regulatory theorem for solutions to the initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity. Combining the continuation of "local" solution argument with the results which have be established earlier, we reached a new result. We can say now that the linear theory is completed. As for the quasi-linear case, the result of our study is still poor. There are many things to do in studying this problem. (2) We studied the nonlinear diffusion equation with strong absorption term. We have been mainly interested in the phenomenon, called the splitting of the support of solutions. Mathematically, this can be regarded as a moving boundary problem. We succeeded in constructing a good scheme for the numerical analysis of the equations. Thus we were able to find a sufficient conclusion under which the splitting of the support of solutions occurs.
  • 基盤研究(C), 1996, 1996, 08640201, 流体力学にあらわれる対称双曲系の特性的境界値問題, 静田 靖; 篠田 正人; 藪田 公三; 宮武 貞夫; 坂本 礼子; 柳沢 卓, 日本学術振興会, 科学研究費助成事業 基盤研究(C), 奈良女子大学, 2400000, 2400000, 静田は線型対称双曲系に対する特性的境界値問題の解が時間について強連続であることを示す際に用いる論法を整理し従来のものと比べて新らしい見通しのよい証明を得た.結果は平成8年7月アテネで開かれた第2回非線型解析国際会議で発表した.坂本は半空間におけるTricomi型方程式の境界値問題を研究し幾つかの結果を得た.宮武は2次元空間でのNavier-Stokes方程式の定常問題に関するKolmogarovの問題を考察し解の分岐を具体的な方法で示すことによって分岐曲線が分岐点において凸であることを証明した.この結果は平成9月3月リスボンで開かれた応用解析に関する国際会議で発表された.藪田は特異積分作用素について研究を行った.篠田はパーコレーションに関する新らしい結果を得て、平成8年9月に奈良女子大学数学教室で行われた非線PDE研究集会で発表した.柳沢は平成8年10月から文部省在外研究員としてヨーロッパに滞在し、特性根の多重度が一定でない場合の対称双曲系に関する結果についてイタリー及びドイツの大学に招かれて講演を行った.
  • 一般研究(C), 1995, 1995, 07640212, 退化双曲型方程式の初期境界値問題, 坂本 礼子; 森藤 紳哉; 薮田 公三; 高橋 世知子; 柳沢 卓; 静田 靖; 宮武 貞夫, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 2100000, 2100000, 2階双曲型方程式が境界で退化するとき、その退化の仕方に応じて問題設定は大きく変わってくることが知られている、本研究においてはある一つの型に限定して、高次導関数を含めたエネルギー不等式を得ることに成功した。これは同じ型の非線型方程式についての局所的解析を可能にするものである。高階の方程式について同様な型が抽出できるかどうかについては今後の課題となっている。
  • 奨励研究(A), 1995, 1995, 07740107, 流体及び電磁流体力学にあらわれる対称双曲系の特性的境界値問題, 柳沢 卓, 日本学術振興会, 科学研究費助成事業 奨励研究(A), 奈良女子大学, 1000000, 1000000, 1.特性的境界値問題特有の現象である「解の法線方向微分の滑らかさの消失」がおこる物理的例として、非線型Maxwell方程式に対するある初期値境界値問題も考えられることがわかった。今後、他の物理的例をさがすことと共に、どの様な方程式と境界条件の関わりにより、この滑らかさの消失がおこるのかを明らかにしていきたい。 2.浅水波方程式.圧縮性Euler方程式の初期値境界値問題を考察するとき、境界で特性根の重複度が一定でない場合が、自然に現われる。本研究では、この様な場合でも、いくつかの制約条件の下では、通常のSobolev空間におけるエネルギー評価が可能となることを明らかにした。しかし、L^2-解の一意的存在を保障する「弱解=強解」なる事実を示すことがまだ出来ていないので、この点を中心に更に研究を進めていきたい。 3.線型圧縮性粘性流体の半平面における非粘性極限に対する考察を進めた。境界層の出現を取り込んだ形での近似解を構成した。
  • 一般研究(C), 1994, 1994, 06640240, 特異積分論とその応用, 薮田 公三; 柳沢 卓; 坂本 礼子; 宮武 貞夫; 高橋 世知子; 藤田 収, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 2100000, 2100000, 1.交付申請書で記した、特異積分論自身の発展に対する寄与として、次の新しい知見を得た。 (1)ベクトル値特異積分であるリトルウッド・ベ-リ-のg函数及びマルチンキ-ヴィッツの函数に対して、リプシッツ空間での有界性に関して、最良の指数1まで成り立つことを論証できた。今までは1/2であったが、見方の見直しと新工夫によって、困難を克服できた。(研究発表論文の一番目に記したもの) (2)(1)での方法を援用して、中国の陸善鎮氏が工夫していた函数空間(中心型一般化リプシッツ空間)でも(1)と同様の結果が成立することを示せた。(研究発表論文の2番目に記したもの、陸善鎮氏、C-MTan氏と共著) (3)(1)に関連して、ル-ジンの面積積分とgラムダ函数に対応するマルチンキ-ヴィッツ函数に対して、p乗可積分空間での有界性に関して、(1)の場合と異なってpにも限界があることを確認出来た。これは昨年末の調和解析セミナーでも部分的に発表したが、今春の学会で発表する。 2.特異積分論の応用面では、直接的なものではないが、オイラー方程式、対称双曲型方程式系に対する初期値境界値問題に対する新知見も得られた。
  • 奨励研究(A), 1993, 1993, 05740095, 正値対称系に対する極大非負な境界値問題, 柳沢 卓, 日本学術振興会, 科学研究費助成事業 奨励研究(A), 奈良女子大学, 1000000, 1000000, 1.境界が重複度一定で特性的な場合の対称双曲系に対する初期値境界値問題に関して。 1)極大非負な境界条件の下で、上記問題の解が高階の可微分性まで含めて滑らかであることを示し、この結果を発表論文リスト[3]にまとめた。又、このとき重みつきの非等方的ソボレフ空間の、トレース定理を明らかにすることが重要となるので、この部分を発表論文リスト[2]としてまとめた。 2)特に初期条件に対する「適合性」について論ずるときには、Dで求めた解の時間変数に関する強連続性を示すことが必要となる。この時間変数に関する強連続性を、Majdaのコ-シ-問題に対して用いた議論と、Rauchの提出した接線方向への軟化子(及びその変形)を使うことにより示すことができたので、現在論文としてまとめている。 2.境界が特性的で、かつその特性根の重複度が一定でない場合の対称双曲系に対する初期値境界値問題に関して。 ある重みを用いたエネルギー法により、たとえ特性根の重複度が変わったとしても、上記問題がH^S-wellpesed(S≧1)となる為の十分条件を与えることができた。また、この十分条件を充たす2×2 systemの具体例を構成した。しかし、磁気流体・浅水波等に対する物理的境界値問題において、どの様な現象が起こっているかについては、何ら満足のいく結果は得られなかった。 3.非圧縮Euler方程式と渦度の方程式に関して。 有界領域における非圧縮Euler流の滑らかさが渦度のmaximum normに支配されることを、境界つきリーマン多様体上の小平-Hodge分解を使って示すことができたので、発表論文リスト[1]にまとめ公表した。
  • 一般研究(C), 1992, 1992, 04640159, 線型および準線型対称双曲系の特性的境界値問題, 静田 靖; 柳沢 卓; 加古 富志雄; 宮武 貞夫; 富崎 松代; 藪田 公三, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 1700000, 1700000, 中心的な課題は線型の対称双曲系に対する初期値境界値問題であるが、これは同時に準線型の方程式系に対しても適用し得るような形で線型の理論を構成することであった。その際導入された函数空間は異方性を持ったソボレフ空間であって、接線方向の微分と法線方向の微分を同等に取り扱わない点が通常のソボレフ空間と異なる。より正確に云えば、接線方向の2回の微分可能が丁度法線方向の1回の微分可能性と対応しているようなソボレフ空間である。この空間における種々の問題とくに、函数積の評価、滑らかな函数との合成函数の評価等々の基礎的な諸事実に対して証明を与えた。また補間空間について考察を行った。その他、一様評価も含めて函数解析的議論について幾つかの改良を行ったので、結果をより洗練された形で定理にまとめることが出来た。以上の議論はつねに結果が特性的ではあるが、多重度は一定と云う仮定の下に行われたものであるが、多重度一定の仮定をはずした場合についても若干のモデルについて計算を行った。この方面の研究はまだ十分に行われているとは云い難いが、今後クローズアップされるであろう。その他確率微分方程式を含めて数理物理学上の問題についても若干の結果を得た。ただし準線型の問題については結果を定理の形にまとめあげることが出来なかった。今後の課題である。
  • 一般研究(C), 1991, 1991, 03640157, フ-リェ積分作用素による特実性の位数の伝播現象の研究, 宮武 貞夫; 高橋 世知子; 加古 富志雄; 柳沢 卓; 藪田 公三; 坂本 礼子, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 1900000, 1900000, 2階の双曲型偏微分方程式に対する初期境界値問題の解,その中でも特に波動方程式のノイマン問題について解の特異性の伝播現象に興味を持ち研究した。具体的に言うと、ノイマン問題のディリクレ問題の解に翻訳して研究した。その理由はディリクレ問題の方が境界デ-タから内部の解への特異性の伝わり方を調べるのが容易である事が一つと,更にイイマンデ-タに対応するディリクレデ-タ(同じ解を与えるデ-タ)を考えることは 解が境界に沿ってどの様に伝わるかを調べることにもなっている事になる。この対応をノイマン作用素と呼ぶことにする。これは半空間の領域の場合には具体的に書き下して研究を進めることが出来る。その場合ノイマン作用素は境界内部における波動作用素口の2/1乗として因果律子満たす様に定めることが出来る。口等の双曲型作用素の分数中は、いまだ研究されたことのない新分野であるが、ラプラス反転公式を使い関数的的藪密な等式計算により、前進波解の1/2又はー1/2を自然に定めることが出来 口^ー1/2により特異性の伝数の伝わる有様を明確に述べることが出来る。その際フレネ積分子一般化した形の積分が有用な動をすることがわかった。これまでの詳価式の研究がより詳しく,必然性子伴っていることが理解された。今後一般領域での研究が進むと思われる。
  • 奨励研究(A), 1989, 1989, 01740093, 磁氣流体力学に現われる準線型対称双曲系の初期境界値問題, 柳沢 卓, 日本学術振興会, 科学研究費助成事業 奨励研究(A), 奈良女子大学, 900000, 900000
  • 一般研究(C), 1988, 1988, 63540124, 完全退化型非線型双曲系の研究, 坂本 礼子; 柳沢 卓; 静田 靖; 岩崎 敷久, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 1000000, 1000000, 1.完全退化型方程式の可解性(線型の場合)を一般論として展開する課題については、ほぼ満足のいく結果が得られ、現在投稿中である。 2.非線型完全退化型方程式の局所可解性に関する課題については、一つの単純な枠組の中ではあるが、非線型性をうまくおさえ込める範ちゅうの存在することがわかった。 3.非線型完全退化型方程式の大域解に関する課題については、2で設定した枠組の中では、解の爆発の様相をきわめて容易にとらえることができることがわかった。1.2の結果をまとめて現在投稿中である。また弱解に関する研究はこれからの課題として残されている。
  • 一般研究(C), 1987, 1988, 62540113, 退化した非線型発展方程式の研究, 坂本 礼子; 柳沢 卓; 長田 博文; 藤田 収; 岩崎 敷久; 静田 靖, 日本学術振興会, 科学研究費助成事業 一般研究(C), 奈良女子大学, 2000000, 2000000, 境界で退化する双曲系の非線型問題については, 流体解析あるいは弾性体解析の方面から具体的なアプローチがなされてきている. 我々の研究グループにおいても, 電磁流体の運動方程式に関連して, いかなる境界条件を与えれば初期境界値問題として適切な問題設定となりうるかという基本問題にかかわる研究を進めてきており, 静田・柳沢らによりいくつかの結果をまとめることができた. また, 今回特に本研究のテーマとしてとりあげた完全退化型の双曲系は, 退化の様相がきわめて単純な場合に焦点をあてようとしたものである. それに関しては, 坂本・岩崎らが線型の問題として系統的研究を進めている. その際, 坂本により導入された一般化された擬微分作用素が道具として有用であることがわかり, その成果は論文としてまとめることができた. このような完全退化型の非線型双曲系としては, ある種の弾性体の運動に関連する方程式系があり, それをかなり一般的にとり扱うことができることがわかってきた. それについては現在論文を準備中である.

Ⅲ.社会連携活動実績

1.公的団体の委員等(審議会、国家試験委員、他大学評価委員,科研費審査委員等)

  • Apr. 2002, Mar. 2005, Society


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