研究者総覧

柳沢 卓 (ヤナギサワ タク)

  • 研究院自然科学系数学領域 教授
  • 教育研究評議会 教育研究評議会評議員
Last Updated :2021/06/23

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学位

  • 博士(理学), 北海道大学

研究キーワード

  • 非線型偏微分方程式 

研究分野

  • 自然科学一般, 基礎解析学

経歴

  • 2010年12月 奈良女子大学理学部教授
  • 2007年04月 - 2010年11月 奈良女子大学大学院人間文化研究科准教授
  • 2003年04月 - 2007年03月 奈良女子大学大学院人間文化研究科助教授
  • 1994年04月 - 2003年03月 奈良女子大学理学部助教授
  • 1991年07月 - 1994年03月 奈良女子大学理学部講師
  • 1986年10月 - 1991年06月 奈良女子大学理学部助手

学歴

  • 1985年04月- 1986年10月 北海道大学大学院 理学研究科博士後期課程 数学専攻
  • 1983年04月- 1985年03月 北海道大学大学院 理学研究科博士前期課程 数学専攻
  • 1979年04月- 1983年03月 北海道大学 理学部 数学科

委員歴

  • 2002年04月 - 2005年03月 日本数学会 岩波「数学」編集委員(非常勤) 日本数学会 society

    学協会

論文

  • The Helmholtz–Weyl decomposition of $$L^r$$ vector fields for two dimensional exterior domains

    Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa

    2021年01月, The Journal of Geometric Analysis, 31 (5), 5146 - 5165, doi;url;url

    研究論文(学術雑誌)

  • A characterization of harmonic L^r-vector fields in two-dimensional exterior domains

    M. Hieber; H. Kozono; A. Seyfert; S. Shimizu; T.Yanagisawa

    2020年01月, The Journal of Geometric Analysis, 30 (4), 3742 - 3759

    研究論文(学術雑誌)

  • 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., 2013年07月, MANUSCRIPTA MATHEMATICA, 141 (3-4), 637 - 662, doi;web_of_science

    研究論文(学術雑誌)

  • 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年, Archive for Rational Mechanics and Analysis, 207 (3), 879 - 905, doi

    研究論文(学術雑誌)

  • L^r Helmholtz Decomposition and Its Application to the Navier-Stokes Equations

    小薗英雄,柳沢卓

    edited by Fanghua Lin and Ping Zhang, 2013年, Lectures on Analysis of Nonlinear Partial Differential Equations: Part 3, \nMorningside Lectures in Mathematics, International Press, 3, 237-290

    研究論文(学術雑誌)

  • 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., 2012年09月, MATHEMATISCHE ANNALEN, 354 (1), 137 - 145, doi;web_of_science

    研究論文(学術雑誌)

  • Analyticity for higher order nonlinear dispersive equations

    林仲夫,友枝恭子,柳沢卓

    2010年, GAKUTO Internat. Ser. Math. Sci. Appl., 32, 111-130

    研究論文(学術雑誌)

  • Global DIV-CURL Lemma in 3D bounded domains

    小薗英雄,柳沢卓

    2009年11月, RIMS Kokyuroku Bessatsu B14, 14, 27-33

    研究論文(研究会,シンポジウム資料等)

  • 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., 2009年11月, PACIFIC JOURNAL OF MATHEMATICS, 243 (1), 127 - 150, web_of_science

    研究論文(学術雑誌)

  • 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., 2009年06月, JOURNAL OF FUNCTIONAL ANALYSIS, 256 (11), 3847 - 3859, doi;web_of_science

    研究論文(学術雑誌)

  • 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., 2009年05月, MATHEMATISCHE ZEITSCHRIFT, 262 (1), 27 - 39, doi;web_of_science

    研究論文(学術雑誌)

  • 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年, INDIANA UNIVERSITY MATHEMATICS JOURNAL, 58 (4), 1853 - 1920, web_of_science

    研究論文(学術雑誌)

  • 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., 2007年03月, OSAKA JOURNAL OF MATHEMATICS, 44 (1), 99 - 119, web_of_science

    研究論文(学術雑誌)

  • Hodge decomposition of L^r-vector fields on a bounded domain and its application to the Navier-Stokes equations

    柳沢卓

    2007年, 数理解析研究所講究録, 1536, 73-86

  • 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., 1999年04月, COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 52 (4), 479 - 541, web_of_science

    研究論文(学術雑誌)

  • The initial boundary value problem for linear symmetric hyperbolic systems with boundary characteristic of constant multiplicity

    M Ohno; Y Shizuta; T Yanagisawa

    1995年07月, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 35 (2), 143 - 210, web_of_science

    研究論文(学術雑誌)

  • NOTE ON GLOBAL EXISTENCE FOR AXIALLY-SYMMETRICAL SOLUTIONS OF THE EULER SYSTEM

    T SHIROTA; T YANAGISAWA

    1994年12月, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 70 (10), 299 - 304, web_of_science

    研究論文(学術雑誌)

  • 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., 1994年09月, TOHOKU MATHEMATICAL JOURNAL, 46 (3), 393 - 401, web_of_science

    研究論文(学術雑誌)

  • A CONTINUATION PRINCIPLE FOR THE 3-D EULER EQUATIONS FOR INCOMPRESSIBLE FLUIDS IN A BOUNDED DOMAIN

    T SHIROTA; T YANAGISAWA

    1993年03月, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 69 (3), 77 - 82, web_of_science

    研究論文(学術雑誌)

  • THE INITIAL BOUNDARY-VALUE-PROBLEMS FOR LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS WITH CHARACTERISTIC BOUNDARY

    M OHNO; Y SHIZUTA; T YANAGISAWA

    1991年06月, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 67 (6), 191 - 196, web_of_science

    研究論文(学術雑誌)

  • 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年, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 136 (1), 119 - 140, web_of_science

    研究論文(学術雑誌)

  • INITIAL BOUNDARY-VALUE PROBLEM FOR THE EQUATIONS OF IDEAL MAGNETO-HYDRO-DYNAMICS WITH PERFECTLY CONDUCTING WALL CONDITION

    T YANAGISAWA; A MATSUMURA

    1988年06月, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 64 (6), 191 - 194, web_of_science

    研究論文(学術雑誌)

  • MIXED PROBLEMS FOR QUASI-LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS

    S KAWASHIMA; T YANAGISAWA; Y SHIZUTA

    1987年09月, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 63 (7), 243 - 246, web_of_science

    研究論文(学術雑誌)

  • The initial boundary value problem for the equations of ideal magneto-hydrodynamics

    Taku Yanagisawa

    1987年, Hokkaido Mathematical Journal, 16 (3), 295 - 314, doi

    研究論文(学術雑誌)

  • L^r-Helmholtz-Weyl decomposition for three dimensional exterior domains

    Mtthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa

    2021年06月03日, Journal of Functional Analysis

MISC

  • 定常MHD方程式に対する境界値問題

    柳沢卓

    2014年07月, 数理解析研究所講究録, 1905, 40-52

  • 多重連結領域における定常Navier-Stokes方程式の境界値問題

    柳沢卓

    2011年, 研究集会PPM2010報告集 \n偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2010, PPM2010-10, 1-9

  • Helmholtz-Weyl分解とその応用

    柳沢卓

    2010年03月, 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, 122-131

  • On the paper "Blows Ups of Complex Solutions of the 3D Navier-Stokes Systems and RG Method" by Ya Sinai and et al.

    柳沢卓

    2008年, 数理解析研究所講究録, 1600, 132-146

  • 理想磁気流体力学の方程式系の初期値境界値問題

    柳沢卓; 松村昭孝

    1990年, 数理解析研究所講究録, 734, 91-105

書籍等出版物

  • Advances in Nonlinear Partial Differential Equations and Stochastics (Series on Advances in Mathematics for Applied Sciences Vol.48)

    柳沢卓 (, 範囲: 編集)

    World Scientific, 1998年01月

講演・口頭発表等

  • On the spaces of harmonic L^r-vector fields over exterior domains

    柳沢卓

    Maximal regularity and nonlinear PDE (RIMS, Kyoto), 2019年03月, RIMS, Kyoto University, Kyoto, Japan, true

    口頭発表(招待・特別)

  • A geometric characterization of the space of harmonic L^r-vector fields over exterior domains

    柳沢卓

    Mathematical Fluid Mechanics and Related Topics (Tokyo Institute of Technology, Tokyo), 2018年09月, Yasuhi Taniuchi et.al., Tokyo Institute of Technology, Ookayama Campus, true

  • Arithmetic-Geometric mean and Newton's method

    柳沢卓

    ミニシンポジュウム(北海道情報大学), 2018年09月, 北海道江別市 北海道情報大学EDタワー, false

  • Characterization of the space of harmonic vector fields over exterior domains

    柳沢卓

    The 35th Kyushu Symposium on Partial Differential Equations (Hakata, Fukuoka), 2018年01月, Shuichi Kawashima, Yoshiyuki Kagei, et.al., Nishijin Plaza, Kyushu University, true

  • 外部領域上の調和ベクトルのなす空間について

    柳沢卓

    第6回岐阜数理科学研究会(岐阜大学サテライトキャンパス,岐阜市), 2017年08月, 岐阜大学サテライトキャンパス 多目的講義室, false

  • On the existence and stability of stationary solutions of MHD equations under the inhomogeneous boundary conditions

    柳沢卓

    The Navier-Stokes Equations and Related Topics (Nagoya University, Nagoya), 2016年03月, Nagoya University, Nagoya, true

  • On the stability of stationary solutions to the MHD equations with large boundary data

    柳沢卓

    RIMS Workshop on Mathematical Analysis in Fluid and Gasdynamics, 2015年07月, RIMS, Kyoto University, Kyoto, true

  • The solvability and stability of boundary value problems for stationary MHD equations

    柳沢卓

    第4回弘前非線形方程式研究会, 2014年12月, 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

  • The boundary value problem for stationary MHD equations

    柳沢卓

    Classical Problems and New Trends in Mathematical Fluid Dynamics on occasion of Professor Konstantin Pileckas' 60th birthday, 2014年10月, Amann, Galdi, Rautmann, Solonnikov 他, Ferrara, Italy, true

  • The solvability and stability of boundary value problems for stationary MHD equations

    柳沢卓

    ICM 2014 Satellite Conference, Mathematical Theory of Gases and Fluids and Related Applications, 2014年08月, Donho Chae, Tai-Ping Liu, Hisashi Okamoto, Chung-Ang University, Seoul, Korea, true

  • The stability of stationary solutions to the MHD equations under the inhomogeneous boundary condition

    柳沢卓

    Fluid Dynamics and Electromagnetism: Theory and Numerical Approximation on occasion of Prof. Paolo Secchi and Alberto Valli 60th birthday, 2014年06月, L. Berselli et. al., Levico Terme, Trento, Italy, true

  • 定常MHD方程式に対する非斉次境界値問題について

    柳沢卓

    大阪市大・大阪府大合同「第19回南大阪応用数学セミナー」, 2014年06月, 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

  • Solvability of boundary value problems of the stationary MHD systems

    柳沢卓

    Recent Advances in PDEs and Applications on occasion of Professor Hugo Beirao da Veiga's 70th birthday, 2014年02月, V. A. Solonnikov, P. Secchi 他, Levico Terme, Trento, Italy, true

  • On the solvability of boundary value problems for the stationary MHD equations with inhomogeneous boundary conditions

    柳沢卓

    Mathematical Analysis of Nonlinear Partial Differential Equations -In honor of Professor Shuichi Kawashima on his sixtieth birthday-, 2013年11月, Yoshiyuki Kagei et.al, Kyushu University Nishijin Plaza, Japan, true

  • Boundary value problems for stationary MHD equations

    柳沢卓

    RIMS研究集会「非圧縮性粘性流体の数理解析」, 2013年11月, 菱田俊明、柴田良弘、清水扇丈, 京都大学数理解析研究所, true

  • On the solvability Navier-Stokes equations with nonhomogeneous boundary condition

    柳沢卓

    Nonlinear Wave Equation and Fluid Mechanics\n-In honor of Professor Thomas C. Sideris on his sixtieth birthday-, 2013年08月, Ogawa Takayoshi et.al., Muroran Institute of Technology, Muroran, Japan, true

  • 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

    柳沢卓

    語ろう数理解析, 2012年01月, 名和,石渡,松本他, 京都大学理学部, false

  • Boundary value problems of the stationary MHD equations and Navier-Stokes equations with Coriolis force

    柳沢卓; Taku Yanagisawa

    Partial Differential Equations in Mathematical Physics and their Numerical Approximation, 2011年09月, Hugo Beirao da Veiga, A, Valli, Levico Terme (Trento), Italy, true

  • Applications of Hodge decomposition to mathematical fluid dynamics

    柳沢卓; Taku Yanagisawa

    The 4th MSJ-SI: Nonlinear Dynamics in Partial Differential Equations, 2011年09月, 日本数学会, 川島秀一他, Kyushu Univ. Hakata, Japan, false

  • On global compensated compactness theorem

    柳沢卓

    International Conference on Fluid and Gas Dynamics, 2011年09月, Yong Zhou, Wuxing Hotel, Jinhua, China, true

  • On the stationary boundary value problems of the Navier-Stokes equations with in and out flow on the boundary

    柳沢卓; Taku Yanagisawa

    7th Internatinal Congress on Industrial and Applied Mathematics, Minisimposium "Recent topics on mathematical analysis for the Navier-Stokes equations", 2011年07月, Shin'ya Matsui and Yoshikazu Giga, Vancouver, BC, Canada, true

  • The solvability of stationary Navier-Stokes equations with inhomogeneous boundary data

    柳沢卓; Taku Yanagisawa

    International Conference on Mathematical Fluid Mechanics and Biomedical Applications, 2011年06月, G.Galdi, Hugo Beirao da Veiga, A. Robertson他, Ponta Delgada, Azores, Portugal, true

  • The stationary Navier-Stokes equations under the inhomogeneous boundary conditions

    柳沢卓; Taku Yanagisawa

    International Workshop on Interaction between Mathematics and Fluid Mechanics, 2011年03月, 鈴木貴,河原源太, 大阪大学基礎工学部, false

  • On global compensated compactness theorem

    柳沢卓; Taku Yanagisawa

    The 3rd Nagoya Workshop on Differential Equations, 2011年02月, 杉本充,菱田俊明, 名古屋大学理1号館, false

  • Global compensated compactness theorem and its applications

    柳沢卓; Taku Yanagisawa

    偏微分方程式と数理物理学(PDE and Mathematical Physics), 2010年11月, 千原浩之他, 京都大学芝蘭会館別館, false

  • 多重連結領域における定常Navier-Stokes方程式の境界値問題

    柳沢卓

    偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2010, 2010年11月, 辻川他, 宮崎大学工学部, false

  • 熱方程式とモーメント問題

    柳沢卓

    PDE白田記念会ミニシンポジウム, 2010年08月, 佐藤剛, 北海道大学大学院理学研究科, false

  • 調和ベクトル場と流体力学等に現れる定常解

    柳沢卓; 柳澤卓

    青葉山勉強会(第5回), 2010年06月, 久保英夫, 東北大学情報科学研究科, false

  • ベクトル場の分解定理とその流体力学への応用

    柳沢卓; 柳澤 卓

    乱流場と非線形構造-数学と流体力学の融合を目指して-, 2010年04月, 金田行雄,小薗英雄,石原卓, 東北大学 数理科学記念館, false

  • Helmholtz-Weyl分解とその応用

    柳沢卓

    日本数学会2010年度年会函数方程式論分科会特別講演, 2010年03月, 日本数学会, 慶応義塾大学, false

  • Asymptotic behavior of solutions to the viscous Burgers equation

    柳沢卓; Taku Yanagisawa

    Linear and Nonlinear Waves, No.7, 2009年11月, T.Nishitani, N.Hayashi, and H.Sunagawa, 大津市, false

  • 境界層方程式について

    柳沢卓

    第2回CESセミナー, 2009年11月, 笹山,松井, 早稲田大学理工学部, false

  • On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition

    柳沢卓; Taku Yanagisawa

    Conference on "Mathematical Physics and PDEs", 2009年09月, Hugo Beirao da Veiga, Alberto Valli, Levico Terme(Trento, Italy), true

  • Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I

    柳沢卓; Taku Yanagisawa

    PDE seminar at Zhejiang Normal University, 2009年05月, Yong Zhou, Zhejiang Normal University, Jinhua, China, true

  • Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data II

    柳沢卓; Taku Yanagisawa

    PDE seminar at Zhejiang Normal University, 2009年05月, Yong Zhou, Zhejiang Normal University, Jinhua, China, true

  • Leray's inequality in 3D domains

    柳沢卓; Taku Yanagisawa

    PDE seminar at Zhejiang Normal University, 2009年05月, Yong Zhou, Zhejiang Normal University, Jinhua, China, true

  • Blow-up criteria for smooth solutions of 3-D compressible Euler equations on a bounded domain

    柳沢卓

    Topics of Fluid Dynamics, 2009年04月, Paolo Secchi, Brescia University, Italy, true

  • Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I, II

    柳沢卓; Taku Yanagisawa

    Series of Lectures at Pisa University (Parts I and II), 2009年03月, Hugo Beirao da Veiga, Pisa University, Italy, true

  • Leray's inequality in 3D domains

    柳沢卓; Taku Yanagisawa

    Series of lectures at Pisa University (Part III), 2009年03月, Hugo Beirao da Veiga, Pisa University, 伊, true

  • Global DIV-CURL lemma

    柳沢卓; Taku Yanagisawa

    Series of lectures at Pisa University (Part IV), 2009年03月, Hugo Beirao da Veiga, Pisa University、伊, true

  • Sinai等によるNavier-Stokes方程式に関する研究の紹介

    柳沢 卓

    早稲田大学PDEセミナー, 2008年11月, 柴田良弘 小澤徹, false

  • Blow-up criteria of smooth solutions for 3-D compressible Euler equations in a bounded domain

    柳沢 卓

    Nonlinear PDE Workshop at Sendai, 2008年11月, 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

  • Helmholtz-Weyl decomposition and its application to compressible Euler flows on a bounded domain

    柳沢卓

    The Banach Center Conference: Parabolic and Navier-Stokes Equations 2008, 2008年09月, H.Amann, Y.Shibata,, Bedlewo, Poland, true

  • Global DIV-CURL Lemma on bounded domains

    柳沢卓

    Workshop on Mathematical Fluid Dynamics, 2008年09月, H.Amann, Darmstadt, Germany, true

  • A decomposition theorem of L^r-vector fields over a bounded domain and its application

    柳沢卓; Taku Yanagisawa

    PDE Seminar, Konstanz University, 2008年09月, R. Racke, Konstanz University, Konstanz, Germany, true

  • Leray's problem on the stationary Navier-Stokes equations and Leray's inequality

    柳沢卓; Taku Yanagisawa

    Navier-Stokes equations:Classical and generalized models, 2008年09月, H.Beirao da Veiga, Centro di Recerca Matematica Ennio De Giorgi, Scoula Normale Superiore di Pisa, Pisa, Italy, true

  • Global DIV-CURL lemma on bounded domains in \R^3

    柳沢 卓

    大阪大学水曜セミナー, 2008年07月, 松村昭孝, 阪大 理学部, false

  • Leary's problem on the stationary Navier-Stokes equations and Leray's inequality

    柳沢 卓

    第2回奈良偏微分方程式研究会, 2008年06月, 柳沢 卓, 奈良女子大学, false

  • Leray's problem on the stationary Navier-Stokes equations and Leray's inequality

    柳沢卓

    PDE Seminar at Fachbereich Mathematik, Technische Universitat Darmstadt, 2008年06月, Reihard Farwig, Darmstadt, Germany, true

  • A Decomposition Theorem and its application to fluid dynamics

    柳沢 卓

    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」, 2008年03月, 岡本久(京大数理解析研), 神戸インスティチュ-ト, false

  • Sinai 等によるNavier-Stokes方程式に関する最近の研究の紹介

    柳沢 卓

    若手による流体力学の基礎方程式研究集会, 2008年01月, 小薗英雄他, 名古屋大学大学院多元数理科学研究科, false

  • On the paper "Blow Ups of Complex Solutions of the 3D Navier-Stokes System and RG Method" by Ya Sinai et al.

    柳沢 卓

    RIMS研究集会「繰りこみ群の数理科学での応用」, 2007年09月, 伊東 恵一(摂南大学・工学部), 京都大学数理解析研究所, false

  • Leray's problem for the stationary Navier-Stokes equations and the harmonic vector fields II

    柳沢 卓

    第32回偏微分方程式論札幌シンポジウム, 2007年08月, 小澤他, 北海道大学, true

  • Decomposition theorems of vector fields and the application to the Navier-Stokes equations

    柳沢卓; Taku Yanagisawa

    Second Workshop on Nonlinear Partial Differential Equations: Analysis, Computation and Application, 2007年06月, Seung Yeal Ha, Yong Jung Kim, Seoul National University, Korea, true

  • On flux problems for the stationary Navier-Stokes equation

    柳沢 卓

    神戸大学解析セミナー, 2007年06月, 足立、高岡, 神戸大学, false

  • The flux problem for stationary Navier-Stokes eqautions in a bounded domain with a mutiply connected boundary

    柳沢 卓

    非線形解析セミナー, 2007年05月, 谷 温之, 慶応大学, false

  • Existence of solutions of nonhomogeneous boundary value problem for stationary Navier-Stokes equations in a bounded domain Nonlinear PDE seminar (Osaka University)

    柳沢 卓

    Nonlinear PDE seminar (Osaka University), 2006年12月, 松村 昭孝, false

  • Nonhomogeneous boundary value problems for the stationary Navier Stokes equations in a multiply connected domain

    柳沢 卓

    第2回 流体と保存則の研究集会, 2006年10月, 西畑 伸也, 東京 (東京工業大学), false

  • 粘性Burgers方程式の解の長時間漸近挙動

    柳沢 卓

    北海道情報大学偏微分方程式セミナー, 2006年09月, 松井 伸也, 札幌 (北海道情報大学), false

  • Hodge decomposition of L^r vector fields on a bounded domain and its application to the Navier Stokes equations

    柳沢卓; Taku Yanagisawa

    RIMS研究集会 「流体と気体の数学解析」, 2006年07月, 隠居良行, 京都, true

  • Asymptotic behavior of solutions to the viscous Burgers equation

    柳沢 卓

    Nolinear PDE seminar (Osaka University), 2006年05月, 松村 昭孝, 大阪大学, false

  • 有界領域上の調和形式の構成とHodge分解定理

    柳沢 卓

    第3回非線形偏微分方程式研究集会, 2006年03月, 三沢 正史、菱田 俊明, 富山県氷見市, false

  • On the decomposition theorem of L^r-vector fields on a bounded domain

    柳沢卓; Taku Yanagisawa

    2006 Korea-Japan Conference on Partial Differential Equations, 2006年03月, HI Jun Choe, Hideo Kozono, Yonsei University, Seoul, Korea, true

  • 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

    柳沢 卓

    解析学談話会(函館みらい大学), 2006年02月, 上見練太朗, 函館, false

  • 有界領域上のベクトル場のHodge分解定理

    柳沢 卓

    北大 PDE Seminar, 2005年11月, 小澤 徹, 札幌, false

  • Asymptotic behavior of solutions to the viscous Burgers eqaution with degenerate initial moments

    柳沢卓; Taku Yanagisawa

    The Fourth International Conference on Nonlinear Analysis and Convex Analysis, 2005年07月, W. Takahashi, T. Tanaka, Okinawa, Japan, true

担当経験のある科目(授業)

  • 現代数物概論A (奈良女子大学)

  • 熱と波動の数学 (奈良女子大学)

  • 数物科学における研究倫理 (奈良女子大学)

  • グローバル理系女性育成国際サマーキャンプ (奈良女子大学)

  • パッサージュ31B(パズルやゲームの中の数学) (奈良女子大学)

  • パッサージュ31A(パズルやゲームの中の数学) (奈良女子大学)

  • 数学物理の歩き方 (奈良女子大学)

  • 数学物理の展開 (奈良女子大学)

  • 数物の展開 (奈良女子大学)

  • 非線型偏微分方程式論 (奈良女子大学)

  • 微分積分学I演習(A) (奈良女子大学)

  • 数物の歩き方 (奈良女子大学)

  • サイエンス・オープンラボⅡ(A) (奈良女子大学)

  • サイエンス・オープンラボⅠ(A) (奈良女子大学)

  • 非線型偏微分方程式論演習 (奈良女子大学)

  • 現象構造解析特論II (奈良女子大学)

  • 現象構造解析特論Ⅰ (奈良女子大学)

  • 線形代数学Ⅰ(B) (奈良女子大学)

  • 微分積分学Ⅰ演習(A) (奈良女子大学)

  • 解析概論Ⅰ演習 (奈良女子大学)

  • 線型代数学概論Ⅰ(A) (奈良女子大学)

  • 卒業研究I (奈良女子大学)

  • 解析概論III演習 (奈良女子大学)

  • 数学特別研究IV (奈良女子大学)

  • 数学特別研究II (奈良女子大学)

  • 数学特別セミナーI (奈良女子大学)

  • 卒業研究II (奈良女子大学)

  • 数学特別セミナーIII (奈良女子大学)

  • 数学特別研究III (奈良女子大学)

  • 数学特別研究I (奈良女子大学)

  • 解析概論I (奈良女子大学)

  • 数学アラカルト (奈良女子大学)

  • 解析概論II演習 (奈良女子大学)

  • 数学特別セミナーII (奈良女子大学)

  • 博士論文執筆指導 (奈良女子大学)

  • 数学特別研究IV (奈良女子大学)

  • 数学特別研究II (奈良女子大学)

  • 数学特別セミナーI (奈良女子大学)

  • 卒業研究II (奈良女子大学)

  • 非線型数学特論演習 (奈良女子大学)

  • 数学特別研究III (奈良女子大学)

  • 数学特別研究I (奈良女子大学)

  • 数学特別セミナーIII (奈良女子大学)

  • 卒業研究I (奈良女子大学)

  • 数学通論I (奈良女子大学)

  • 数学の歩き方 (奈良女子大学)

  • 数学の展開 (奈良女子大学)

  • 現代数学概論 (奈良女子大学)

  • 非線型数学特論 (奈良女子大学)

  • 微分積分学概論IIA (奈良女子大学)

  • 非線型解析学演習 (奈良女子大学)

  • 解析概論演習I (奈良女子大学)

  • 非線型解析学 (奈良女子大学)

  • 解析概論IV演習 (奈良女子大学)

  • 解析概論I演習 (奈良女子大学)

  • 解析概論Ⅰ (奈良女子大学)

  • 専門職論(理学部) (奈良女子大学)

  • 関数方程式 (奈良女子大学)

  • 解析概論Ⅱ演習 (奈良女子大学)

  • 積分論Ⅱ (奈良女子大学)

  • 積分論I (奈良女子大学)

  • 微分積分学概論IA (奈良女子大学)

所属学協会

  • 日本数学会

  • Japan Mathematical Sociaty



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