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

Research Project

Project/Area Number 24540173
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNara 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 *help
¥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.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (14 results)

All 2014 2013 2012 Other

All Journal Article (5 results) (of which Open Access: 1 results,  Peer Reviewed: 4 results) Presentation (9 results) (of which Invited: 8 results)

  • [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

    • Related Report
      2014 Annual Research Report
    • Open Access
  • [Journal Article] L^r Helmholtz decomposition and its application to the Navier-Stokes equations2013

    • 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

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global compensated compactness theorem for general differential operators of first order2013

    • 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

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized Lax-Milgram theorem in Banach spaces and its application to the elliptic system of boundary value problems2013

    • 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

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Leray's inequality in general multi-connected domains in R^n2012

    • 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

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] The solvability and stability of boundary value problems for stationary MHD equations2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The boundary value problem for stationary MHD equations2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The solvability and stability of boundary value problems for stationary MHD equations2014

    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
  • [Presentation] The stability of stationary solutions to the MHD equations under the inhomogeneous boundary condition2014

    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2013 Research-status Report
    • 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
    • Related Report
      2013 Research-status Report
    • 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
    • Related Report
      2013 Research-status Report
    • 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
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2013-05-31   Modified: 2019-07-29  

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