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Mathematical analysis on overhanging waves

Research Project

Project/Area Number 20740080
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionTokyo University of Science

Principal Investigator

OGAWA Masao  Tokyo University of Science, 理工学部, 助教 (50408704)

Project Period (FY) 2008 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords非線形偏微分方程式 / 解析学
Research Abstract

The motion of water waves is a prime research subject in fluid dynamics. This motion is usually formulated as the free boundary problem for an irrotational, incompressible and ideal fluid. It is known that the temporally local solution for this problem exists, even if the waves overhang. On the other hand, the motion of the waves of the ocean is rotational. Therefore, we are interested in the water-wave problem without the assumption of the irrotational motion. First, the author has analyzed the linearized problem. This problem is different from the one in the case that the amplitude of the surface is not large. After that, by the result for the linearized problem and the symmetry of the equations, the existence of the temporally local solution for the water-wave problem has been shown.

Report

(3 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • Research Products

    (8 results)

All 2009 2008

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (6 results)

  • [Journal Article] Well-posedness for water wave problem with vorticity2009

    • Author(s)
      Masao Ogawa
    • Journal Title

      Nonlinear Analysis Series A: Theory, Methods and Applications 71巻

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Well-posedness for water wave problem with vorticity2009

    • Author(s)
      小川聖雄
    • Journal Title

      Nonlinear Analysis Series A : Theory, Methods and Applications 71巻

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 水の波の問題に対する数学解析2009

    • Author(s)
      小川聖雄
    • Organizer
      京都産業大学理学部公開セミナー
    • Place of Presentation
      京都
    • Year and Date
      2009-12-05
    • Related Report
      2009 Final Research Report
  • [Presentation] 水の波の問題に対する数学解析2009

    • Author(s)
      小川聖雄
    • Organizer
      理学部公開セミナー
    • Place of Presentation
      京都産業大学
    • Year and Date
      2009-12-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] Rotational motion of an inviscid incompressible fluid with free boundary2008

    • Author(s)
      Masao Ogawa
    • Organizer
      Navier-Stokes equations: Classical and generalized models
    • Place of Presentation
      イタリア
    • Year and Date
      2008-09-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Rotational motion of an inviscid incompressible fluid with free boundary2008

    • Author(s)
      小川聖雄
    • Organizer
      Navier-Stokes equations : Classical and generalized models
    • Place of Presentation
      イタリアピサ
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Rotational motion of an inviscid incompressible fluid with free boundary2008

    • Author(s)
      Masao Ogawa
    • Organizer
      The Fifth World Congress of Nonlinear Analysts
    • Place of Presentation
      アメリカ
    • Year and Date
      2008-07-02
    • Related Report
      2009 Final Research Report
  • [Presentation] Rotational motion of an inviscid incompressible fluid with free boundary2008

    • Author(s)
      小川聖雄
    • Organizer
      The Fifth World Congress of Nonlinear Analysts
    • Place of Presentation
      アメリカオーランド
    • Year and Date
      2008-07-02
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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