The development of the unified analytical method to hydrodynamical and electromagnetic phenomena based on decomposition theorems

• Project/Area Number: 24540173
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara Women's University
• Principal Investigator: YANAGISAWA Taku 奈良女子大学, 自然科学系, 教授 (30192389)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 分解定理 / 境界値問題 / 流体力学 / 電磁気学 / MHD方程式 / 磁気流体力学 / MHD / Navier-Stokes方程式 / 磁気流体力学方程式 / 定常問題 / 非粘性極限 / 弱解

Outline of Final Research Achievements

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.

Research Products

• [Journal Article] 定常MHD方程式に対する境界値問題 (2014)
  • Author(s): 柳澤 卓
  • Journal Title: 数理解析研究所講究録 Volume: 1905 Pages: 40-52
  • Open Access
• [Journal Article] L^r Helmholtz decomposition and its application to the Navier-Stokes equations (2013)
  • Author(s): Hideo Kozono, Taku Yanagisawa
  • Journal Title: Lectures on Analysis of Nonlinear Partial Differential Equations, Morningside Lectures in Mathematics, International Press Volume: Part 3 Pages: 237-290
  • Peer Reviewed
• [Journal Article] Global compensated compactness theorem for general differential operators of first order (2013)
  • Author(s): Kozono, H., Yanagisawa, T.
  • Journal Title: Arch. Rational Mech. Anal. Volume: 207 Issue: 3 Pages: 879-905
  • DOI: 10.1007/s00205-012-0583-7
  • Peer Reviewed
• [Journal Article] Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems (2013)
  • Author(s): Kozono, H., Yanagisawa, T.
  • Journal Title: Manuscripta Math. Volume: 141 Issue: 3-4 Pages: 637-662
  • DOI: 10.1007/s00229-012-0586-6
  • Peer Reviewed
• [Journal Article] Leray's inequality in general multi-connected domains in R^n (2012)
  • Author(s): H. Kozono, R. Farwig, T. Yanagisawa
  • Journal Title: Mathematische Annalen(online first) Volume: 354 Issue: 1 Pages: 137-145
  • DOI: 10.1007/s00208-011-0716-6
  • Peer Reviewed
• [Presentation] The solvability and stability of boundary value problems for stationary MHD equations (2014)
  • Author(s): 柳澤 卓
  • Organizer: 第4回弘前非線形方程式研究会
  • Place of Presentation: 弘前大学 （青森県弘前市）
  • Year and Date: 2014-12-06
  • Invited
• [Presentation] The boundary value problem for stationary MHD equations (2014)
  • Author(s): Taku Yanagisawa
  • Organizer: Classical Problems and New Trends in Mathematical Fluid Dynamics on occasion of Professor Konstantin Pileckas' 60th birthday
  • Place of Presentation: Ferrara (Italy)
  • Year and Date: 2014-10-02
  • Invited
• [Presentation] The solvability and stability of boundary value problems for stationary MHD equations (2014)
  • Author(s): Taku Yanagisawa
  • Organizer: ICM 2014 Satellite Conference, Mathematical Theory of Gases and Fluids and Related Applications
  • Place of Presentation: Seoul (Korea)
  • Year and Date: 2014-08-12
  • Invited
• [Presentation] 定常MHD方程式に対する非斉次境界値問題について (2014)
  • Author(s): 柳澤 卓
  • Organizer: 大阪市大・大阪府大合同「第19回南大阪応用数学セミナー」
  • Place of Presentation: 大阪府立大学 （大阪府堺市）
  • Year and Date: 2014-06-28
• [Presentation] The stability of stationary solutions to the MHD equations under the inhomogeneous boundary condition (2014)
  • Author(s): Taku Yanagisawa
  • Organizer: Fluid Dynamics and Electromagnetism: Theory and Numerical Approximation on occasion of Prof. Paolo Secchi and Alberto Valli 60th birthday
  • Place of Presentation: Levico Terme (Italy)
  • Year and Date: 2014-06-05
  • Invited
• [Presentation] Solvability of boundary value problems of the stationary MHD systems
  • Author(s): Taku Yanagisawa
  • Organizer: Recent Advances in PDEs and Applications on occasion of Professor Hugo Beirao da Veiga's 70th birthday
  • Place of Presentation: Bellavista Relax Hotel, Levico Terme (Trento), Italy
  • Invited
• [Presentation] Boundary value problems for stationary MHD equations
  • Author(s): Taku Yanagisawa
  • Organizer: Mathematical Analysis of Viscous Incompressible Fluid, RIMS Symposium
  • Place of Presentation: RIMS, Kyoto University (Kyoto), Japan
  • Invited
• [Presentation] On the solvability of boundary value problems for the stationary MHD equations with inhomogeneous boundary conditions
  • Author(s): Taku Yanagisawa
  • Organizer: Mathematical Analysis of Nonlinear Partial Differential Equations -In honor of Professor Shuichi Kawashima on his sixtieth birthday-
  • Place of Presentation: Nishijin Plaza, Kyushu University (Hakata), Japan
  • Invited
• [Presentation] On the solvability Navier-Stokes equations with nonhomogeneous boundary condition
  • Author(s): Taku Yanagisawa
  • Organizer: Nonlinear Wave Equation and Fluid Mechanics -In honor of Professor Thomas C. Sideris on his sixtieth birthday-
  • Place of Presentation: Education Research Hall 2, Q402 Muroran Institute of Technology (Muroran), Japan
  • Invited