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Analysis of the Stokes operator with some boundary conditions of Neumann type and its application

Research Project

Project/Area Number 22740084
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionUniversity of Toyama

Principal Investigator

YAMAGUCHI Norikazu  富山大学, 人間発達科学部, 准教授 (50409679)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsStokes作用素 / Navier-Stokes方程式 / MHD方程式 / 安定性 / 処罰法 / 数学的正当化 / 解析半群 / ナヴィエ・ストークス方程式 / 誤差評価 / 解析学 / 非線形偏微分方程式 / ナヴィエ・ストーク方程式 / 粘性流体
Research Abstract

We studied the Navier-Stokes equations and MHD equations arising from fluid mechanics. On the MHD equations, we obtained a stability theorem of exponential type in three-dimensional bounded and simply connected domain. We also studied validity of the penalty method for the Navier-Stokes equations in the whole space. For such a problem, we obtained a mathematical justification result by method of analytic semigroup theory

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (14 results)

All 2013 2012 2011 2010 Other

All Journal Article (1 results) Presentation (13 results) (of which Invited: 3 results)

  • [Journal Article] Mathematical justification of the penalty method for viscous incompressible fluid flows2013

    • Author(s)
      Norikazu Yamaguchi
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1830 Pages: 127-142

    • Related Report
      2012 Final Research Report
  • [Presentation] Navier-Stokes方程式系に対する処罰法の半群理論による正当化について2013

    • Author(s)
      山口範和
    • Organizer
      神戸大学解析セミナー
    • Place of Presentation
      神戸大学
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] A mathematical justification of the penalty method for the Navier-Stokes equations2013

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      International Conference on the mathematical fluid dynamics
    • Place of Presentation
      ホテル日航奈良
    • Related Report
      2012 Final Research Report
  • [Presentation] Mathematical justification of the penalty method for viscous incompressible fluid flow2012

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      流体と気体の数学解析
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Final Research Report
  • [Presentation] A mathematical justification of the penalty method for the Stokes and Navier-Stokes equations2012

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      Prabolic and Navier-Stokes equations 2012,Stefan Banach
    • Place of Presentation
      国際数学センター(ベドレヴォ・ポーランド)
    • Related Report
      2012 Final Research Report
  • [Presentation] On a mathematical justification of the penalty method for the Stokes and Navier-Stokes equations2011

    • Author(s)
      山口範和
    • Organizer
      4^<th> Japanese-Germany Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-11-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Remarks on the penalty method for the Stokes and Navier-Stokes equations2011

    • Author(s)
      山口範和
    • Organizer
      The 3^<rd> China-Japan Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      西北大学(西安・中国)
    • Year and Date
      2011-10-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] On a mathematical justification of the penalty method for the Stokes and Navier-Stokes equations2011

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      4th Japanese-Germany Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Final Research Report
  • [Presentation] On some stability theorem of the MHD equations.2010

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      Regularity Aspects of PDEs, Stefan Banach
    • Place of Presentation
      国際数学センター(ポーランド)
    • Related Report
      2012 Final Research Report
  • [Presentation] Remarks on the penalty method for the Stokes and Navier-Stokes equations2010

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      The 3rd China-Japan Workshop on Mathematical Topics from Fluid Mechanics
    • Place of Presentation
      西北大学(西安・中国)
    • Related Report
      2012 Final Research Report
  • [Presentation] On some stability theorem of the MHD equations2010

    • Author(s)
      山口範和
    • Organizer
      Regularity Aspects of PDEs
    • Place of Presentation
      ステファン・バナッハ国際数学センター(Bedlewo・Poland)
    • Related Report
      2010 Annual Research Report
  • [Presentation] A mathematical justification of the penalty method for the Navier-Stokes equations

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      International Conference on the Mathematical Fluid Dynamics
    • Place of Presentation
      ホテル日航奈良
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] A mathematical justification of the penalty method for the Navier-Stokes equations

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      Parabolic and Navier-Stokes equations 2012
    • Place of Presentation
      Banach国際数学センター(ポーランド)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Mathematical justification of the penalty method for the viscous incompressible fluid flows

    • Author(s)
      Norikazu Yamaguchi
    • Organizer
      流体と気体の数学解析
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2010-11-30   Modified: 2019-07-29  

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