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Analysis of singular perturbations of the Navier-Stokes equations

Research Project

Project/Area Number 11640211
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHokkaido Information University

Principal Investigator

MATSUI Sin'ya  Hokkaido Information University, Faculty of Business Administration and Information Science, Associated Professor, 経営情報学部, 助教授 (50219367)

Co-Investigator(Kenkyū-buntansha) YANAGISAWA Taku  Nara Women's University, Faculty of Science, Associated Professor, 理学部, 助教授 (30192389)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsNavier-Stokes equations / Plandtl equations / Boundary Layer / Zero Viscosity Limit / Blasius equation / Prandtl方程式 / 粘性消滅問題 / 遅れを持った非線形常微分方程式 / 非定常境界層方程式
Research Abstract

In this project I researched jointly with Professor Yanagisawa, Professor Giga, Professor Ishimura and others. The papers which we published are stated in References. In these papers we studied the Navier-Stokes equations in the whole space or in the half space and studied zero viscosity limit of the compressible viscous fluid in the half plane. The pre-print papers are the followings :
(with Ishimura, N.) On blow-up solutions of the Blasius equation.
(with Giga, Y. and Sasayama, T.) Blow up rate for a semilinear heat equation with subcritical nonlinearity.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] 松井伸也, 他: "On estimates in Hardy spaces for the Stokes flow in a half space"Mathematische Zeitschrift. 231, No.2. 383-396 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 松井 伸也, 他: "On the Cauchy problem for the Navier-Stokes equations with non decaying initial data"Advances in Fluid Dynamics, ed. By Paolo Maremonti. Quaderni di mathematic a Vol.4. 28-68 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 柳沢卓, 他: "Zero-Viscosity Limit of the Linearized Navier-Stokes Equations for a Compressible Viscous Fluid in the Half-Plane"Communications of Pure and Applied Mathematics. Vol.52. 479-541 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 松井伸也, 他: "Existence of a forward self-similar stagnation flow of the Navier-Stokes equations"Japan Journal of Industrial and Applied Mathematics. Vol.17, No.1. 19-25 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 松井伸也, 他: "Remarks on the uniqueness of bounded solution of the Navier-Stokes equations"Nonlinear Analysis. Vol.47. 4151-4156 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 松井伸也, 他: "Global existence of two-dimensional Navier-Stokes flow with nondecaying initial data"Journal of Mathematical Fluid Mechanics. Vol.3. 302-315 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Giga Y., Matsui S. and Shimizu Y.: "On estimates in Hardy spaces for the Stokes flow in a half space"Math. Z.. 231 No.2. 383-396 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Giga Y., Inui K. and Matsui S: "On the Cauchy problem for the Navier-Stokes equations with non decaying initial data"Advances in Fluid Dynamics ed. By Maremonti, P., ARACNE.. 28-68 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Xin Z. and Yanagisawa T.: "Zero-Viscosity Limit of the Linearized Navier-Stokes Equations for a Compressible Viscous Fluid in the Half-Plane"CPAM. Vol. LII. 479-541 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Ishikawa M. and Matsui S: "Existence of a forward. Self-similar stagnation flow of the Navier-Stokes equations"JJIAM. Vol. 17 No. 1. 19-25 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Giga Y., Inui K., Kato J. and Matsui S.: "Remarks on the uniqueness of bounded solution of the Navier-Stokes equations"Nonlinear Anal.. Vol. 47. 4151-4156 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Giga Y., Matsui S. and Sawada O: "Global existence of two-dimensional Navier-Stokes flow with nondecaying initial data"J. of Math. Fluid Mech.. Vol. 3. 302-315 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 松井伸也, 他: "On estimates in Hardy spaces for the Stokes flow in a half space"Mathematische Zeitschrift. 231,No.2. 383-396 (1999)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松井伸也, 他: "On the Cauchy problem for the Navier-Stokes equations with non decaying initial data"Advances in Fluid Dynamics, ed.By Paolo Maremonti. Quaderni di mathematic a Vol.4. 28-68 (1999)

    • Related Report
      2001 Annual Research Report
  • [Publications] 柳沢卓, 他: "Zero-Viscosity Limit of the Linearized Navier-Stokes Equations for a Compressible Viscous Fluid in the Half-Plane"Communications of Pure and Applied Mathematics. Vol.52. 479-541 (1999)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松井伸也, 他: "Existence of a forward self-similar stagnation flow of the Navier-Stokes equations"Japan Journal of Industrial and Applied Mathematics. Vol.17,No.1. 19-25 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松井伸也, 他: "Remarks on the uniqueness of bounded solution of the Navier-Stokes equations"Nonlinear Analysis. Vol.47. 4151-4156 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松井伸也, 他: "Global existence of two-dimensional Navier-Stokes flow with nondecaying initial data"Journal of Mathematical Fluid Mechanics. Vol.3. 302-315 (2001)

    • Related Report
      2001 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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