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Singular perturbation analysis of viscous fluid equations with Coriolis force term in the meteorological point of view

Research Project

Project/Area Number 17540201
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 Shin'ya  Hokkaido Information University, Faculty of media information science, Professor (50219367)

Co-Investigator(Kenkyū-buntansha) GIGA Yoshikazu  The University of Tokyo, Graduate School of Mathematical Science, Professor
MAHALOV Alex  Arizona State University, Department of Mathematics, Professor
SAAL Jurgen  Hokkaido Information University, Department of Mathematics and Statistics, Doctor
INUI Katsuya  Hokkaido Information University, Faculty of Science and Technology, Doctor
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,830,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsThe Navier-Stokes eauations / Fluid motion in a rotating filed / Singular parturbation / Metrological phenomena / コリオリカ / テイラー・プラウドマンの定理 / 非圧縮性粘性流体 / 微小摂動の全体構造への影響 / 非線形偏微分方程式 / Coriolis力 / 空間無限での非減衰解
Research Abstract

In this project, we analyzed existence and singular limit behavior of solutions for the Navier-Stokes equations with Coriolis force term in 3 dimensional whole space, 3 dimensional half space and Poincare domain :
1. We discussed the Cauchy problem for the 3dimensional Navier-Stokes equations with Coriolis force term. Here, for initial data we employed a vector of a class of solenoidal bounded vector fields. In this case the existence time of solution is depends on the Coriolis force parameter (a half of angular velocity speed around rotating axis). (Joint work with Giga, Inui and Mahalov)
2. If initial date for the Cauchy problem of our problem is a Fourier inversed image of Radon measure whose support does not include the origin, the existence time of a solution is NOT independent of Coriolis parameter. (Joint work with Giga, Inui and Mahalov)
3. We considered initial boundary problem in 3 dimensional half space. The solution of our problem is constructed around the Eckman boundary layer solution, whose tangential component is not required to be zero and whose normal component is close to be Eckman boundary layer solution at normal space component infinity in the norm of L^p. ((Joint work with Giga, Inui, Mahalov and Saal))
4. The stationary solutions of our problem in 3 dimensional Poincare domain are not almost be unique in L^2 space. If Coriolis force parameter goes to infinity, all stationary solution is close to the state which is independ of the direction of rotating axis. This singular perturbation is in H^2 (strong convergence). Furthermore if our domain is simple, stationary solutions convergence to the mean with respect to rotating axis of a singular perturbation limit. (Joint work with Inui and Mahalov)

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (16 results)

All 2008 2007 2006 2005 Other

All Journal Article (10 results) (of which Peer Reviewed: 5 results) Presentation (6 results)

  • [Journal Article] On the Navier-Stokes stationary flow with Coriolis force term2008

    • Author(s)
      松井 伸也
    • Journal Title

      PAMM 7(印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Rotating Navier-Stokes equations in R^3_+ with initial data nondecaying at infinity:The Eckman boundary layer problem2007

    • Author(s)
      松井 伸也
    • Journal Title

      Archive for Rational Mechanics and analysis 186

      Pages: 177-224

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Rotating Navier-Stokes equations in R^3_+ with initial data nondecreasing at infinity : The Ekman boundary layer problem2007

    • Author(s)
      Giga, Y., Inui, K., Mahalov, A., Matsui, S., Saal, J
    • Journal Title

      Archive for Rational Mechanics and Analysis Vol. 186

      Pages: 177-224

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Rotating Navier-Stokes Equations in R^3_+with Initial Data Nondecreasing at Infinity: The Ekman Boundary Layer Problem2007

    • Author(s)
      Y.Giga, K.Inui, A.Mahalov, S.Matsui, and J.Saal
    • Journal Title

      Archive for Rational Mechanics and Analysis 186

      Pages: 177-224

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Navier-Stokes equations in a rotating frame in R^3 with initial data nondecaying at infinity2006

    • Author(s)
      松井 伸也
    • Journal Title

      Hokkaido Mathematical Journal 35

      Pages: 321-364

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Navier-Stokes equations in a Rotating frame2006

    • Author(s)
      Giga, Y., Inui, K., Mahalov, A., Matsui, S
    • Journal Title

      Hokkaido Mathematical Journal Vol. 35

      Pages: 321-364

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Navier-Stokes Equations in a Rotating Framein R^3 with Initial Data Nondecreasing at Infinity2006

    • Author(s)
      Giga, Inui, Mahalov, Matsui
    • Journal Title

      Hokkaido Math. J. Vol.35

      Pages: 321-364

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Uniform local solvability for the Navier-Stokes equations with the Corio lis force2005

    • Author(s)
      松井 伸也
    • Journal Title

      Methods and Application of Analysis 12

      Pages: 381-394

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Uniform local solvability for he Navier Stokes equations with the Coriolis force2005

    • Author(s)
      Giga, Y., Inui, K., Mahalov, A., Matsui, S
    • Journal Title

      Methods and Applications pf Analysis Vol. 12

      Pages: 381-394

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the Navier-Stokes stationary flow with Coriolis force term

    • Author(s)
      Inui, K., Mahalov, A., Matsui, S
    • Journal Title

      PMM (To appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Navier-Stokes equations with Coriolis force term2007

    • Author(s)
      松井 伸也
    • Organizer
      第32回偏微分方程式札幌シンポジウム
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-08-25
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Navier-Stokes equations with Coriolis force term2007

    • Author(s)
      Matsui, S
    • Organizer
      32nd Sapporo Sympojium on PDE
    • Place of Presentation
      Hokkaido University
    • Year and Date
      2007-08-25
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Navier-Stokes equations with Coriolis force term2007

    • Author(s)
      松井 伸也
    • Organizer
      The 32^<nd> Sapporo Symposium on PDE
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-08-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the stationary Navier-Stokes flow with Coriolis force term2007

    • Author(s)
      松井 伸也
    • Organizer
      6th International congress for Industrial and Applied Mathematics(ICIAM 2007)
    • Place of Presentation
      ETH Zurich
    • Year and Date
      2007-07-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the stationary Nvier-Stokes flow with Coriolis force term2007

    • Author(s)
      Matsui, S
    • Organizer
      6th International Congress for Industrial and applied Mathematics(ICIAM 2007)
    • Place of Presentation
      ETH Zurich
    • Year and Date
      2007-07-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the Stationary Navier-Stokes Flow with Coriolis Force Term2007

    • Author(s)
      松井 伸也
    • Organizer
      ICIAM 2007
    • Place of Presentation
      ETH Zurich
    • Year and Date
      2007-07-20
    • Related Report
      2007 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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