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2005 Fiscal Year Final Research Report Summary

Study on the change of patterns of vortices and waves in fluid flow.

Research Project

Project/Area Number 15340054
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MIYAKAWA Tetsuro  Kanazawa Universit, Graduate School of Natural Science and Technology, Professor, 自然科学研究科, 教授 (10033929)

Co-Investigator(Kenkyū-buntansha) FUKUMOTO Yasuhide  Kyushu University, Graduate School of Mathematics, Professor, 数理学研究院, 教授 (30192727)
IGUCHI Tatsuo  Tokyo Institute of Technology, Graduate School of Natural Science and Technology, Associate Professor, 理工学研究科, 助教授 (20294879)
HISHIDA Toshiaki  Niigata University, Faculty of Natural Science, Associate Professor, 自然科学系, 助教授 (60257243)
OMATA Seiro  Kanazawa Universit, Graduate School of Natural Science and Technology, Professor, 自然科学研究科, 教授 (20214223)
HATAUE Itaru  Kanazawa Universit, Graduate School of Natural Science and Technology, Professor, 自然科学研究科, 教授 (50218476)
Project Period (FY) 2003 – 2005
KeywordsNavier-Stokes equations / Initial value problem / Free surface / Group-symmetry / Stability / Vortex filament / Vortex ring / Singular integral
Research Abstract

MIYAKAWA studied the flows of a viscous incompressible fluid in two and three-dimensional exterior domains and clarified explicit relationship between the space-time decay rates of flows and the symmetry of solutions of the equations of motion. He obtained almost complete results in the case of two space dimensions. FUKUMOTO studied the evolution of viscous vortices, applying the singular perturbation method to the non-local induction model, and obtained new results on the topological change of vortex filaments and rings. HISHIDA studied the viscous flow around a rotating body and proved for the first time the existence of stationary and nonstationary flows by finding a new class of singular integral operators. He also gave a new existence result for flows in domains with apertures. IGUCHI applied the method for treating free-surface problem to the equation of one-dimensional gas dymanics and gave a completely new approach to this problem which has wide applications to equations of similar types. He also classified the shape of free surfaces associated with shallow water flow with periodic bottom, applying the bifurcation theory.

  • Research Products

    (24 results)

All 2006 2004 2003 Other

All Journal Article (24 results)

  • [Journal Article] Nonstationary Navier-Stokes flows in a two-dimensional exterior domain with rotational symmetries2006

    • Author(s)
      Cheng He
    • Journal Title

      Indiana University Mathematics Journal 55(掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] D'Alembert's paradox and the integrability of pressure for two-dimensional in compressible Euler flows2006

    • Author(s)
      Tetusro Miyakawa
    • Journal Title

      Kyushu Journal of Mathematics 60(掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Nonstationary Navier-Stokes flows in a two-dimensional exterior domain with rotational symmetries.2006

    • Author(s)
      Cheng HE, Tetsuro MIYAKAWA
    • Journal Title

      Indiana University Mathematics Journal 55(to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] D'Alembert's paradox and the integrability of pressure for two-dimensional incompressible Euler flows in an exterior domain.2006

    • Author(s)
      Tetsuro MIYAKAWA
    • Journal Title

      Kyushu Journal of Mathematics 60(to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Conservation laws of circulation and helicity as Noether's theorem2004

    • Author(s)
      Yasuhide Fukumoto
    • Journal Title

      Computational Fluid Dynamics Journal 13

      Pages: 417-421

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The nonstationary Stokes and Navier-Stokes flows through an aperture2004

    • Author(s)
      Toshiaki Hishida
    • Journal Title

      Advances in Mathematical Fluid Mechanics 3

      Pages: 79-123

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] L^g theory of a singular "winding" operator arising from fluid dynamics2004

    • Author(s)
      Reinhard Farwig
    • Journal Title

      Pacific Journal of Mathematics 215

      Pages: 297-312

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Conservation laws of circulation and helicity as Noether's theorem.2004

    • Author(s)
      Yasuhide FUKUMOTO
    • Journal Title

      Computational Fluid Dynamics Journal 13

      Pages: 417-421

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The nonstationary Stokes and Navier-Stokes flows through an aperture.2004

    • Author(s)
      Toshiaki HISHIDA
    • Journal Title

      Advances in Mathematical Fluid Mechanics 3

      Pages: 79-123

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] L^q-theory of a singular "winding" integral operator arising from fluid dynamics.2004

    • Author(s)
      Reinhard FARWIG, Toshiaki HISHIDA, Detlef Muller
    • Journal Title

      Pacific Journal of Mathematics 215

      Pages: 297-312

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On L^1-summability and asymptotic profiles of smooth solutions to Navier-Stokes equations in a 3D exterior domain2003

    • Author(s)
      Cheng He
    • Journal Title

      Mathematische Zeitschrift 245

      Pages: 387-417

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] The three-dimensional instability of a strained vortex tube revisited2003

    • Author(s)
      Yasuhide Fukumoto
    • Journal Title

      Journal of Fluid Mechanics 493

      Pages: 287-318

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Short-wavelength stability analysis of thin vortex rings2003

    • Author(s)
      Yuji Hattori
    • Journal Title

      Physics of Fluids 15

      Pages: 3151-3163

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On steady surface waves over a periodic bottom2003

    • Author(s)
      Tatsuo Iguchi
    • Journal Title

      Wave Motion 37

      Pages: 219-239

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Existence theory for hyperbolic systems of conservation laws with general flux-functions2003

    • Author(s)
      Tatsuo Iguchi
    • Journal Title

      Archives for Rational Mechanics and Analysis 168

      Pages: 165-244

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On L^1-summability and asymptotic profiles of smooth solutions to Navier-Stokes equations in a 3D exterior domain.2003

    • Author(s)
      Cheng HE, Tetsuro MIYAKAWA
    • Journal Title

      Mathematische Zeitschrift 245

      Pages: 387-417

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The three-dimensional instability of a strained vortex tube revisited.2003

    • Author(s)
      Yasuhide FUKUMOTO
    • Journal Title

      Journal of Fluid Mechanics 493

      Pages: 287-318

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Short-wavelength stability analysis of thin vortex rings.2003

    • Author(s)
      Yuji HATTORI, Yasuhide FUKUMOTO
    • Journal Title

      Physics of Fluids 15

      Pages: 3151-3163

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On steady surface waves over a periodic bottom : relations between the pattern of imperfect bifurcation and the shape of the bottom.2003

    • Author(s)
      Tatsuo IGUCHI
    • Journal Title

      Wave motion 37

      Pages: 219-239

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Existence theory for hyperbolic systems of conservation laws with general flux-functions.2003

    • Author(s)
      Tatsuo IGUCHI, Phillipe G.LeFLOCH
    • Journal Title

      Archives for Rational Mechanics and Analysis 168

      Pages: 165-244

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] L^g estimates of weak solutions to the stationary stokes equations around a rotating body

    • Author(s)
      Toshiaki Hishida
    • Journal Title

      Journal of the Mathematical Society of Japan (掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A Mathematical justification of the forced Korteweg-de Vries equation

    • Author(s)
      Tatsuo Iguchi
    • Journal Title

      Kyushu Journal of Mathematic (掲載予定)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] L^q estimates of weak solutions to the stationary Stokes equations around a rotating body.

    • Author(s)
      Toshiaki HISHIDA
    • Journal Title

      Journal of the Mathematical Society of Japan (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A mathematical justification of the forced Korteweg-de Vries equation for capillary-gravity waves.

    • Author(s)
      Tatsuo IGUCHI
    • Journal Title

      Kyushu Journal of Mathematics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2007-12-13  

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