査読あり, 英語, The Journal of Geometric Analysis, 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05月, 31, 5, 5146, 5165, 研究論文(学術雑誌), 10.1007/s12220-020-00473-4
査読あり, 英語, The Journal of Geometric Analysis, A Characterization of Harmonic $$L^r$$-Vector Fields in Two-Dimensional Exterior Domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, 2020年12月, 30, 4, 3742, 3759, 研究論文(学術雑誌), 10.1007/s12220-019-00216-0
査読あり, 英語, MANUSCRIPTA MATHEMATICA, 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, 141, 3-4, 637, 662, 研究論文(学術雑誌), 10.1007/s00229-012-0586-6
査読あり, 英語, 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年, 207, 3, 879, 905, 研究論文(学術雑誌), 10.1007/s00205-012-0583-7
査読あり, 英語, 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, 小薗英雄,柳沢卓, edited by Fanghua Lin and Ping Zhang, 2013年, 3, 237-290, 研究論文(学術雑誌)
査読あり, 英語, MATHEMATISCHE ANNALEN, 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, 354, 1, 137, 145, 研究論文(学術雑誌), 10.1007/s00208-011-0716-6
査読あり, 英語, GAKUTO Internat. Ser. Math. Sci. Appl., Analyticity for higher order nonlinear dispersive equations, 林仲夫,友枝恭子,柳沢卓, 2010年, 32, 111-130, 研究論文(学術雑誌)
査読あり, 英語, RIMS Kokyuroku Bessatsu B14, Global DIV-CURL Lemma in 3D bounded domains, 小薗英雄,柳沢卓, 2009年11月, 14, 27-33, 研究論文(研究会,シンポジウム資料等)
査読あり, 英語, PACIFIC JOURNAL OF 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., 2009年11月, 243, 1, 127, 150, 研究論文(学術雑誌)
査読あり, 英語, JOURNAL OF FUNCTIONAL ANALYSIS, 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, 256, 11, 3847, 3859, 研究論文(学術雑誌), 10.1016/j.jfa.2009.01.010
査読あり, 英語, MATHEMATISCHE ZEITSCHRIFT, 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, 262, 1, 27, 39, 研究論文(学術雑誌), 10.1007/s00209-008-0361-2
査読あり, 英語, INDIANA UNIVERSITY MATHEMATICS 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年, 58, 4, 1853, 1920, 研究論文(学術雑誌)
査読あり, 英語, 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., 2007年03月, 44, 1, 99, 119, 研究論文(学術雑誌)
査読無し, 英語, 数理解析研究所講究録, 京都大学, Hodge decomposition of L^r-vector fields on a bounded domain and its application to the Navier-Stokes equations, 柳沢卓, 2007年, 1536, 73-86, 86
査読あり, 英語, COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 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, 52, 4, 479, 541, 研究論文(学術雑誌)
査読あり, 英語, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 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, 35, 2, 143, 210, 研究論文(学術雑誌)
査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, NOTE ON GLOBAL EXISTENCE FOR AXIALLY-SYMMETRICAL SOLUTIONS OF THE EULER SYSTEM, T SHIROTA; T YANAGISAWA, 1994年12月, 70, 10, 299, 304, 研究論文(学術雑誌)
査読あり, 英語, TOHOKU MATHEMATICAL JOURNAL, 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, 46, 3, 393, 401, 研究論文(学術雑誌)
査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, A CONTINUATION PRINCIPLE FOR THE 3-D EULER EQUATIONS FOR INCOMPRESSIBLE FLUIDS IN A BOUNDED DOMAIN, T SHIROTA; T YANAGISAWA, 1993年03月, 69, 3, 77, 82, 研究論文(学術雑誌)
査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, THE INITIAL BOUNDARY-VALUE-PROBLEMS FOR LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS WITH CHARACTERISTIC BOUNDARY, M OHNO; Y SHIZUTA; T YANAGISAWA, 1991年06月, 67, 6, 191, 196, 研究論文(学術雑誌)
査読あり, 英語, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 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, 136, 1, 119, 140, 研究論文(学術雑誌)
査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 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, 64, 6, 191, 194, 研究論文(学術雑誌)
査読あり, 英語, PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, MIXED PROBLEMS FOR QUASI-LINEAR SYMMETRICAL HYPERBOLIC SYSTEMS, S KAWASHIMA; T YANAGISAWA; Y SHIZUTA, 1987年09月, 63, 7, 243, 246, 研究論文(学術雑誌)
査読あり, 英語, Hokkaido Mathematical Journal, The initial boundary value problem for the equations of ideal magneto-hydrodynamics, Taku Yanagisawa, 1987年, 16, 3, 295, 314, 研究論文(学術雑誌), 10.14492/hokmj/1381518181
査読あり, 英語, Journal of Functional Analysis, L^r-Helmholtz-Weyl decomposition for three dimensional exterior domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, 2021年10月, 281, 8, 109144, 109144, 研究論文(学術雑誌), 10.1016/j.jfa.2021.109144
査読あり, 英語, Calculus of Variations and Partial Differential Equations, Stationary Navier–Stokes equations under inhomogeneous boundary conditions in 3D exterior domains, Matthias Hieber; Hideo Kozono; Anton Seyfert; Senjo Shimizu; Taku Yanagisawa, 2021年07月, 60, 5, 研究論文(学術雑誌), 10.1007/s00526-021-02050-1
査読あり, 英語, 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, 2022年05月19日, 32, 研究論文(学術雑誌)
査読あり, 日本語, 数学, 3次元L^r-ベクトル場に対するHelmholtz-Weyl分解, 小薗英雄; 清水扇丈; 柳澤卓, 2023年01月, 75, 1, 1, 30
柳沢卓, Maximal regularity and nonlinear PDE (RIMS, Kyoto), On the spaces of harmonic L^r-vector fields over exterior domains, 2019年03月, 英語, RIMS, Kyoto University, Kyoto, Japan, 国際会議
柳沢卓, Mathematical Fluid Mechanics and Related Topics (Tokyo Institute of Technology, Tokyo), A geometric characterization of the space of harmonic L^r-vector fields over exterior domains, 2018年09月, 英語, Yasuhi Taniuchi et.al., Tokyo Institute of Technology, Ookayama Campus, 国際会議
柳沢卓, ミニシンポジュウム(北海道情報大学), Arithmetic-Geometric mean and Newton's method, 2018年09月, 日本語, 北海道江別市 北海道情報大学EDタワー, 国内会議
柳沢卓, The 35th Kyushu Symposium on Partial Differential Equations (Hakata, Fukuoka), Characterization of the space of harmonic vector fields over exterior domains, 2018年01月, 英語, Shuichi Kawashima, Yoshiyuki Kagei, et.al., Nishijin Plaza, Kyushu University, 国際会議
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), 外部領域上の調和ベクトルのなす空間について, 2017年08月, 日本語, 岐阜大学サテライトキャンパス 多目的講義室, 国内会議
柳沢卓, The Navier-Stokes Equations and Related Topics (Nagoya University, Nagoya), On the existence and stability of stationary solutions of MHD equations under the inhomogeneous boundary conditions, 2016年03月, 英語, Nagoya University, Nagoya, 国際会議
柳沢卓, RIMS Workshop on Mathematical Analysis in Fluid and Gasdynamics, On the stability of stationary solutions to the MHD equations with large boundary data, 2015年07月, 英語, RIMS, Kyoto University, Kyoto, 国際会議
柳沢卓, 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, 2014年12月, 日本語, 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」, 国内会議
柳沢卓, 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, 2014年10月, 英語, Amann, Galdi, Rautmann, Solonnikov 他, Ferrara, Italy, 国際会議
柳沢卓, 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, 2014年08月, 英語, Donho Chae, Tai-Ping Liu, Hisashi Okamoto, Chung-Ang University, Seoul, Korea, 国際会議
柳沢卓, 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, 2014年06月, 英語, L. Berselli et. al., Levico Terme, Trento, Italy, 国際会議
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」, 定常MHD方程式に対する非斉次境界値問題について, 2014年06月, 日本語, 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, 国内会議
柳沢卓, 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, 2014年02月, 英語, V. A. Solonnikov, P. Secchi 他, Levico Terme, Trento, Italy, 国際会議
柳沢卓, 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, 2013年11月, 英語, Yoshiyuki Kagei et.al, Kyushu University Nishijin Plaza, Japan, 国際会議
柳沢卓, RIMS研究集会「非圧縮性粘性流体の数理解析」, Boundary value problems for stationary MHD equations, 2013年11月, 英語, 菱田俊明、柴田良弘、清水扇丈, 京都大学数理解析研究所, 国際会議
柳沢卓, 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, 2013年08月, 英語, Ogawa Takayoshi et.al., Muroran Institute of Technology, Muroran, Japan, 国際会議
柳沢卓, 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, 2012年01月, 日本語, 名和,石渡,松本他, 京都大学理学部, 国内会議
柳沢卓; 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, 2011年09月, 英語, Hugo Beirao da Veiga, A, Valli, Levico Terme (Trento), Italy, 国際会議
柳沢卓; Taku Yanagisawa, The 4th MSJ-SI: Nonlinear Dynamics in Partial Differential Equations, Applications of Hodge decomposition to mathematical fluid dynamics, 2011年09月, 英語, 日本数学会, 川島秀一他, Kyushu Univ. Hakata, Japan, 国内会議
柳沢卓, International Conference on Fluid and Gas Dynamics, On global compensated compactness theorem, 2011年09月, 英語, Yong Zhou, Wuxing Hotel, Jinhua, China, 国際会議
柳沢卓; 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, 2011年07月, 英語, Shin'ya Matsui and Yoshikazu Giga, Vancouver, BC, Canada, 国際会議
柳沢卓; Taku Yanagisawa, International Conference on Mathematical Fluid Mechanics and Biomedical Applications, The solvability of stationary Navier-Stokes equations with inhomogeneous boundary data, 2011年06月, 英語, G.Galdi, Hugo Beirao da Veiga, A. Robertson他, Ponta Delgada, Azores, Portugal, 国際会議
柳沢卓; Taku Yanagisawa, International Workshop on Interaction between Mathematics and Fluid Mechanics, The stationary Navier-Stokes equations under the inhomogeneous boundary conditions, 2011年03月, 英語, 鈴木貴,河原源太, 大阪大学基礎工学部, 国内会議
柳沢卓; Taku Yanagisawa, The 3rd Nagoya Workshop on Differential Equations, On global compensated compactness theorem, 2011年02月, 英語, 杉本充,菱田俊明, 名古屋大学理1号館, 国内会議
柳沢卓; Taku Yanagisawa, 偏微分方程式と数理物理学(PDE and Mathematical Physics), Global compensated compactness theorem and its applications, 2010年11月, 英語, 千原浩之他, 京都大学芝蘭会館別館, 国内会議
柳沢卓, 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, 2010年11月, 日本語, 辻川他, 宮崎大学工学部, 国内会議
柳沢卓, 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, 2010年08月, 日本語, 佐藤剛, 北海道大学大学院理学研究科, 国内会議
柳沢卓; 柳澤卓, 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, 2010年06月, 日本語, 久保英夫, 東北大学情報科学研究科, 国内会議
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-, ベクトル場の分解定理とその流体力学への応用, 2010年04月, 日本語, 金田行雄,小薗英雄,石原卓, 東北大学 数理科学記念館, 国内会議
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, Helmholtz-Weyl分解とその応用, 2010年03月, 日本語, 日本数学会, 慶応義塾大学, 国内会議
柳沢卓; Taku Yanagisawa, Linear and Nonlinear Waves, No.7, Asymptotic behavior of solutions to the viscous Burgers equation, 2009年11月, 英語, T.Nishitani, N.Hayashi, and H.Sunagawa, 大津市, 国内会議
柳沢卓, 第2回CESセミナー, 境界層方程式について, 2009年11月, 日本語, 笹山,松井, 早稲田大学理工学部, 国内会議
柳沢卓; Taku Yanagisawa, Conference on "Mathematical Physics and PDEs", On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition, 2009年09月, 英語, Hugo Beirao da Veiga, Alberto Valli, Levico Terme(Trento, Italy), 国際会議
柳沢卓; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I, 2009年05月, 英語, Yong Zhou, Zhejiang Normal University, Jinhua, China, 国際会議
柳沢卓; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data II, 2009年05月, 英語, Yong Zhou, Zhejiang Normal University, Jinhua, China, 国際会議
柳沢卓; Taku Yanagisawa, PDE seminar at Zhejiang Normal University, Leray's inequality in 3D domains, 2009年05月, 英語, Yong Zhou, Zhejiang Normal University, Jinhua, China, 国際会議
柳沢卓, Topics of Fluid Dynamics, Blow-up criteria for smooth solutions of 3-D compressible Euler equations on a bounded domain, 2009年04月, 英語, Paolo Secchi, Brescia University, Italy, 国際会議
柳沢卓; 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, 2009年03月, 英語, Hugo Beirao da Veiga, Pisa University, Italy, 国際会議
柳沢卓; Taku Yanagisawa, Series of lectures at Pisa University (Part III), Leray's inequality in 3D domains, 2009年03月, 英語, Hugo Beirao da Veiga, Pisa University, 伊, 国際会議
柳沢卓; Taku Yanagisawa, Series of lectures at Pisa University (Part IV), Global DIV-CURL lemma, 2009年03月, 英語, Hugo Beirao da Veiga, Pisa University、伊, 国際会議
柳沢 卓, 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, 2008年11月, 日本語, 柴田良弘 小澤徹, 国内会議
柳沢 卓, Nonlinear PDE Workshop at Sendai, Blow-up criteria of smooth solutions for 3-D compressible Euler equations in a bounded domain, 2008年11月, 日本語, 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, 国内会議
柳沢卓, The Banach Center Conference: Parabolic and Navier-Stokes Equations 2008, Helmholtz-Weyl decomposition and its application to compressible Euler flows on a bounded domain, 2008年09月, 英語, H.Amann, Y.Shibata,, Bedlewo, Poland, 国際会議
柳沢卓, Workshop on Mathematical Fluid Dynamics, Global DIV-CURL Lemma on bounded domains, 2008年09月, 英語, H.Amann, Darmstadt, Germany, 国際会議
柳沢卓; Taku Yanagisawa, PDE Seminar, Konstanz University, A decomposition theorem of L^r-vector fields over a bounded domain and its application, 2008年09月, 英語, R. Racke, Konstanz University, Konstanz, Germany, 国際会議
柳沢卓; Taku Yanagisawa, Navier-Stokes equations:Classical and generalized models, Leray's problem on the stationary Navier-Stokes equations and Leray's inequality, 2008年09月, 英語, H.Beirao da Veiga, Centro di Recerca Matematica Ennio De Giorgi, Scoula Normale Superiore di Pisa, Pisa, Italy, 国際会議
柳沢 卓, 大阪大学水曜セミナー, Global DIV-CURL lemma on bounded domains in \R^3, 2008年07月, 日本語, 松村昭孝, 阪大 理学部, 国内会議
柳沢 卓, 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, 2008年06月, 日本語, 柳沢 卓, 奈良女子大学, 国内会議
柳沢卓, PDE Seminar at Fachbereich Mathematik, Technische Universitat Darmstadt, Leray's problem on the stationary Navier-Stokes equations and Leray's inequality, 2008年06月, 英語, Reihard Farwig, Darmstadt, Germany, 国際会議
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」, A Decomposition Theorem and its application to fluid dynamics, 2008年03月, 日本語, 岡本久(京大数理解析研), 神戸インスティチュ-ト, 国内会議
柳沢 卓, 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, 2008年01月, 日本語, 小薗英雄他, 名古屋大学大学院多元数理科学研究科, 国内会議
柳沢 卓, 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., 2007年09月, 日本語, 伊東 恵一(摂南大学・工学部), 京都大学数理解析研究所, 国内会議
柳沢 卓, 第32回偏微分方程式論札幌シンポジウム, Leray's problem for the stationary Navier-Stokes equations and the harmonic vector fields II, 2007年08月, 英語, 小澤他, 北海道大学, 国際会議
柳沢卓; 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, 2007年06月, 英語, Seung Yeal Ha, Yong Jung Kim, Seoul National University, Korea, 国際会議
柳沢 卓, 神戸大学解析セミナー, On flux problems for the stationary Navier-Stokes equation, 2007年06月, 日本語, 足立、高岡, 神戸大学, 国内会議
柳沢 卓, 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, 2007年05月, 日本語, 谷 温之, 慶応大学, 国内会議
柳沢 卓, 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), 2006年12月, 日本語, 松村 昭孝, 国内会議
柳沢 卓, 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, 2006年10月, 日本語, 西畑 伸也, 東京 (東京工業大学), 国内会議
柳沢 卓, 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, 2006年09月, 日本語, 松井 伸也, 札幌 (北海道情報大学), 国内会議
柳沢卓; Taku Yanagisawa, RIMS研究集会 「流体と気体の数学解析」, Hodge decomposition of L^r vector fields on a bounded domain and its application to the Navier Stokes equations, 2006年07月, 英語, 隠居良行, 京都, 国際会議
柳沢 卓, Nolinear PDE seminar (Osaka University), Asymptotic behavior of solutions to the viscous Burgers equation, 2006年05月, 日本語, 松村 昭孝, 大阪大学, 国内会議
柳沢 卓, 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, 2006年03月, 日本語, 三沢 正史、菱田 俊明, 富山県氷見市, 国内会議
柳沢卓; Taku Yanagisawa, 2006 Korea-Japan Conference on Partial Differential Equations, On the decomposition theorem of L^r-vector fields on a bounded domain, 2006年03月, 英語, HI Jun Choe, Hideo Kozono, Yonsei University, Seoul, Korea, 国際会議
柳沢 卓, 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, 2006年02月, 日本語, 上見練太朗, 函館, 国内会議
柳沢 卓, 北大 PDE Seminar, 有界領域上のベクトル場のHodge分解定理, 2005年11月, 日本語, 小澤 徹, 札幌, 国内会議
柳沢卓; 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, 2005年07月, 英語, W. Takahashi, T. Tanaka, Okinawa, Japan, 国際会議
Taku Yanagisawa, 国内, 北海道情報大学 偏微分方程式セミナー, n次元熱方程式に対する長時間漸近形と修正熱核, 口頭発表(一般), 2024年02月18日, 2024年02月18日, 2024年02月18日, 英語
Taku Yanagisawa, 国内, 新潟駅前 応用解析研究会, n次元熱方程式に対する長時間漸近形と修正熱核, 口頭発表(招待・特別), 2024年01月20日, 2024年01月20日, 2024年01月21日, 英語
南香名, 国内, 日本数学会2023年度秋季総合分科会函数方程式論分科会, n次元熱方程式の長時間漸近形, 口頭発表(一般), 2023年09月21日, 2023年09月20日, 2023年09月23日, 日本語