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

2012 Fiscal Year Final Research Report

• 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
• 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

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] 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
  • Year and Date: 20130300
• [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
  • Year and Date: 20130200
• [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)
  • Year and Date: 20120900
• [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
  • Year and Date: 20120700
• [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
  • Year and Date: 20111100
• [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)
  • Year and Date: 20101000
• [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)
  • Year and Date: 20100900