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

• Project/Area Number: 22740084
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: University 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: ¥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)
• Keywords: Stokes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

Research Products

• [Journal Article] Mathematical justification of the penalty method for viscous incompressible fluid flows (2013)
  • 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
• [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
• [Presentation] A mathematical justification of the penalty method for the Navier-Stokes equations (2013)
  • Author(s): Norikazu Yamaguchi
  • Organizer: International Conference on the mathematical fluid dynamics
  • Place of Presentation: ホテル日航奈良
• [Presentation] Mathematical justification of the penalty method for viscous incompressible fluid flow (2012)
  • 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
• [Presentation] A mathematical justification of the penalty method for the Stokes and Navier-Stokes equations (2012)
  • 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)
• [Presentation] On a mathematical justification of the penalty method for the Stokes and Navier-Stokes equations (2011)
  • 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
• [Presentation] Remarks on the penalty method for the Stokes and Navier-Stokes equations (2011)
  • 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
• [Presentation] On a mathematical justification of the penalty method for the Stokes and Navier-Stokes equations (2011)
  • Author(s): Norikazu Yamaguchi
  • Organizer: 4th Japanese-Germany Workshop on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学
• [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)
• [Presentation] Remarks on the penalty method for the Stokes and Navier-Stokes equations (2010)
  • 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)
• [Presentation] On some stability theorem of the MHD equations (2010)
  • 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)
• [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
  • 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）
  • 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
  • Invited