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Asymptotic analysis of water waves over a periodically oscillating bottom

Research Project

Project/Area Number 24340030
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Global analysis
Research InstitutionKeio University

Principal Investigator

IGUCHI Tatsuo  慶應義塾大学, 理工学部, 教授 (20294879)

Co-Investigator(Kenkyū-buntansha) TANI Atusi  慶應義塾大学, 理工学部, 名誉教授 (90118969)
TAKAYAMA Masahiro  慶應義塾大学, 理工学部, 助教 (90338252)
Co-Investigator(Renkei-kenkyūsha) KAGEI Yoshiyuki  九州大学, 大学院数理学研究院, 教授 (80243913)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywords水の波 / 水面波 / 浅水波 / 浅水波近似 / 長波長近似 / 流体 / 関数方程式 / 変分構造 / Euler-Lagrange方程式 / 国際研究者交流 / フランス / 浅水波方程式 / Green-Naghdi方程式 / Boussinesq方程式 / 国際情報交換 / 中国 / 関数方程式論
Outline of Final Research Achievements

We considered the shallow water and long wave approximations for water waves over a periodically oscillating bottom, whose horizontally spatial scale is ε. We analyzed the homogenized limit (ε→0) of the solution to the shallow water equations by the method of multiple scales and determined explicitly the behavior of the solution. We also analyzed the homogenized limit and the long wave limit at the same time to a Boussinesq type equation. Moreover, we clarified the structure of a model for water waves which is obtained by the use of the variational structure.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (31 results)

All 2015 2014 2013 2012 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (23 results) (of which Invited: 13 results) Remarks (1 results)

  • [Journal Article] A shallow water approximation for water waves over a moving bottom2015

    • Author(s)
      Hiroyasu Fujiwara and Tatsuo Iguchi
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 印刷中

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Solvability of the initial value problem to a model system for water waves2015

    • Author(s)
      Yuuta Murakami and Tatsuo Iguchi
    • Journal Title

      Kodai Mathematical Journal

      Volume: 印刷中

    • NAID

      130005475910

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Motion of a vortex filament with axial flow in the half space2014

    • Author(s)
      Masashi Aiki and Tatsuo Iguchi
    • Journal Title

      Annales de l'Institut Henri Poincare (C) Non Linear Analysis

      Volume: 31 Issue: 6 Pages: 1311-1335

    • DOI

      10.1016/j.anihpc.2013.09.004

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Initial value problem for water waves and shallow water and long wave approximations2013

    • Author(s)
      Tatsuo Iguchi
    • Journal Title

      Nankai Series in Pure, Applied Mathematics and Theoretical Physics

      Volume: 10 Pages: 24-40

    • DOI

      10.1142/9789814449755_0003

    • ISBN
      9789814449748, 9789814449755
    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Motion of a vortex filament in the half-space2012

    • Author(s)
      Aiki Masashi, Tatsuo Iguchi
    • Journal Title

      Nonlinear Analysis. Theory, Methods & Applications

      Volume: 75 Pages: 5180-5185

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Solvability of an initial-boundary value problem for a second order parabolic system with a third order dispersion term2012

    • Author(s)
      Aiki Masashi, Tatsuo Iguchi
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 44 Pages: 3388-3411

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Small-time Existence of a Strong Solution of Primitive Equations for the Ocean2012

    • Author(s)
      Hirotada Honda, Atusi Tani
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 35 Pages: 97-138

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] A mathematical justification of the thin film approximation for the flow down an inclined plane2015

    • Author(s)
      上野 大樹,井口 達雄
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学(東京都・千代田区)
    • Year and Date
      2015-03-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] A mathematical justification of the thin film approximation for the flow down an inclined plane2015

    • Author(s)
      上野 大樹,井口 達雄
    • Organizer
      現象解析特別セミナー 第7回
    • Place of Presentation
      茨城大学 教育学部(茨城県・水戸市)
    • Year and Date
      2015-03-17
    • Related Report
      2014 Annual Research Report
  • [Presentation] Solvability of a model system for water wave to a model system for water waves2015

    • Author(s)
      井口 達雄
    • Organizer
      The 7th Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学(愛知県・名古屋市)
    • Year and Date
      2015-03-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] A mathematical justification of the thin film approximation for the flow down an inclined plane2015

    • Author(s)
      上野 大樹,井口 達雄
    • Organizer
      研究集会「若手のための偏微分方程式と数学解析」
    • Place of Presentation
      福岡大学 セミナーハウス(福岡県・福岡市)
    • Year and Date
      2015-02-09
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Solvability of a model system for water wave to a model system for water waves2015

    • Author(s)
      井口 達雄
    • Organizer
      Mathematical Analysis on Fluid Dynamics and Conservation Laws
    • Place of Presentation
      東京工業大学(東京都・目黒区)
    • Year and Date
      2015-01-23
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Solvability of the initial value problem to a model system for water waves2014

    • Author(s)
      井口 達雄
    • Organizer
      慶應力学系セミナー
    • Place of Presentation
      慶應義塾大学理工学部(神奈川県・横浜市)
    • Year and Date
      2014-11-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 水の波の方程式2014

    • Author(s)
      井口 達雄
    • Organizer
      非線形偏微分方程式 冬の学校 '14 in 札幌
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Year and Date
      2014-11-21 – 2014-11-22
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Solvability of a model system for water wave to a model system for water waves2014

    • Author(s)
      井口 達雄
    • Organizer
      Linear and Nonlinear Waves, No.12
    • Place of Presentation
      ピアザ淡海 滋賀県立県民交流センター(滋賀県・大津市)
    • Year and Date
      2014-11-13
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Motion of a Vortex Filament in an External Flow2014

    • Author(s)
      相木 雅史,井口 達雄
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      広島大学(広島県・東広島市)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] Solvability of the initial value problem to a model system for water waves2014

    • Author(s)
      井口 達雄
    • Organizer
      京都大学NLPDEセミナー
    • Place of Presentation
      京都大学理学部(京都府・京都市)
    • Year and Date
      2014-07-11
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the thin film approximation for the flow of a viscous incompressible fluid down an inclined plane2014

    • Author(s)
      上野 大樹,井口 達雄
    • Organizer
      10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Madrid (Spain)
    • Year and Date
      2014-07-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] On the thin film approximation for the flow of a viscous incompressible fluid down an inclined plane2014

    • Author(s)
      上野 大樹,井口 達雄
    • Organizer
      RIMS研究集会「Mathematical Analysis in Fluid and Gas Dynamics」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2014-07-03
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Motion of a Vortex Filament in an External Flow2014

    • Author(s)
      相木 雅史,井口 達雄
    • Organizer
      RIMS共同研究「線形および非線形分散型方程式に関する最近の進展」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2014-05-21
    • Related Report
      2014 Annual Research Report
  • [Presentation] Solvability of the initial value problem to a model system for water waves2014

    • Author(s)
      井口 達雄
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学理学部(東京都・新宿区)
    • Year and Date
      2014-04-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Motion of a Vortex Filament in an External Flow2014

    • Author(s)
      相木 雅史,井口 達雄
    • Organizer
      神楽坂解析セミナー
    • Place of Presentation
      東京理科大学理学部(東京都・新宿区)
    • Year and Date
      2014-04-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Shallow water approximations for water waves2013

    • Author(s)
      井口達雄
    • Organizer
      Seminar on Nonlinear PDE in Nara
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2013-03-11
    • Related Report
      2012 Research-status Report
  • [Presentation] Free Boundary Problem of Magnetohydrodynamics2013

    • Author(s)
      谷温之
    • Organizer
      第30回九州における偏微分方程式研究集会
    • Place of Presentation
      福岡大学
    • Year and Date
      2013-01-30
    • Related Report
      2012 Research-status Report
  • [Presentation] On the thin film approximation for the flow of a viscous incompressible fluid down an inclined plane2013

    • Author(s)
      Tatsuo Iguchi
    • Organizer
      International Conference: Mathematical Analysis of Nonlinear Partial Differential Equations
    • Place of Presentation
      九州大学西新プラザ
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Solvability of the initial value problem to a model system for water waves2013

    • Author(s)
      Tatsuo Iguchi
    • Organizer
      RIMS Workshop "Kinetic Modeling and Related Equations: Conference in Memory of Seiji Ukai''
    • Place of Presentation
      京都大学楽友会館
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 水の波の数学解析2013

    • Author(s)
      井口達雄
    • Organizer
      第35回発展方程式若手セミナー
    • Place of Presentation
      ヒルズサンピア山形
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Solvability of the initial value problem to a model system for water waves2013

    • Author(s)
      Tatsuo Iguchi
    • Organizer
      The Second Pacific Rim Mathematical Association (PRIMA) Congress
    • Place of Presentation
      Shanghai Jiao Tong University
    • Related Report
      2013 Research-status Report
  • [Presentation] Solvability of the initial value problem to a model system for water waves2013

    • Author(s)
      Tatsuo Iguchi
    • Organizer
      The 8th Japanese-German International Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 水の波の浅水波近似について2012

    • Author(s)
      井口達雄
    • Organizer
      弘前解析セミナー
    • Place of Presentation
      弘前大学
    • Year and Date
      2012-11-30
    • Related Report
      2012 Research-status Report
  • [Remarks] 井口研究室ホームページ

    • URL

      http://www.math.keio.ac.jp/~iguchi/

    • Related Report
      2014 Annual Research Report

URL: 

Published: 2012-04-24   Modified: 2019-07-29  

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