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Mathematical analysis of spin-coat

Research Project

Project/Area Number 23840016
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionGifu University

Principal Investigator

SAWADA Okihiro  岐阜大学, 工学部, 准教授 (80451433)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords偏微分方程式 / スピンコート / ナヴィエ・ストークス / 国際研究者交流 / 国際情報交換 / 回転流体運動 / 最大正則性定理 / 自由境界値問題 / ニュートンポリゴン
Research Abstract

We study the mathematical analysis of the spin-coat model withthe heat convection. We propose the suitable model, and proved the local existence and uniqueness of mild solutions to the rotating Navier-Stokes equations coupled with the heat transport equation in a layer-like domain with Coriolis forth, centrifugal forth, surface tension, partially-slip boundary conditions, acceleration of gravity and heat convection terms. In particular, we give the precise estimates for the gradient of the pressure terms. Also, the mathematical validity of obtained solutions is investigated. From the new estimates for the solutions to the linearized equations, we can improve the existence time of locally-in-time mild solutions to the nonlinear problem. Analysis of this model coupled with latent heat effects is important regarding as the first step for the rigorous proof of the instability theory.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • Research Products

    (15 results)

All 2013 2012 2011

All Presentation (15 results) (of which Invited: 4 results)

  • [Presentation] Asymptotic behavior of renormalization solutions of the incompressible fluid2013

    • Author(s)
      澤田宙広
    • Organizer
      第5回名古屋微分方程式研究集会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2013-03-11
    • Related Report
      2012 Final Research Report
  • [Presentation] Asymptotic behavior of renormalization solutions of the incompressible fluid2013

    • Author(s)
      澤田 宙広
    • Organizer
      第5回名古屋微分方程式研究集会
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] スピン・コート現象の数理解析 -最大正則性定理の応用-2012

    • Author(s)
      澤田宙広
    • Organizer
      北大PDEセミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-12-12
    • Related Report
      2012 Final Research Report
  • [Presentation] スピン・コート現象の数理解析-最大正則性定理の応用-2012

    • Author(s)
      澤田宙広
    • Organizer
      北海道大学理学部・偏微分方程式セミナー
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2012-12-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] ナヴィエ・ストークス方程式の臨界空間での非適切性定理2012

    • Author(s)
      澤田宙広
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-21
    • Related Report
      2012 Final Research Report
  • [Presentation] Ill-posedness theory and norm-inflation argument of the 3-D Navier-Stokes equations in the critical Space2012

    • Author(s)
      澤田宙広
    • Organizer
      Parabolic and Navier-Stokes Equations 2012
    • Place of Presentation
      バナッハ研究所(ポーランド)
    • Year and Date
      2012-09-03
    • Related Report
      2012 Final Research Report
  • [Presentation] Ill-posedness and norm-inflation arguments of the 3-D Navier-Stokes2012

    • Author(s)
      澤田宙広
    • Organizer
      Workshop of complex fluids
    • Place of Presentation
      ダルムシュタット工科大学(ドイツ)
    • Year and Date
      2012-07-12
    • Related Report
      2012 Final Research Report
  • [Presentation] スピンコート現象の数理モデルにおける最大正則性定理の応用2012

    • Author(s)
      澤田宙広
    • Organizer
      早大流体数学セミナー
    • Place of Presentation
      早大流体数学セミナー
    • Year and Date
      2012-02-06
    • Related Report
      2012 Final Research Report
  • [Presentation] スピンコート現象の数理モデルにおける最大正則性定理の応用2012

    • Author(s)
      澤田宙広
    • Organizer
      早稲田大学理工学部・流体数学セミナー
    • Place of Presentation
      早稲田大学理工学部
    • Year and Date
      2012-02-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Ill-posedness and norm-in ation arguments of the 3-D Navier-Stokes2012

    • Author(s)
      澤田 宙広
    • Organizer
      Workshop on Complex Fluids
    • Place of Presentation
      ダルムシュタット工科大学(ドイツ)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ill-posedness theory and norm-in ation argument of the 3-D Navier-Stokes equations in the critical space2012

    • Author(s)
      澤田 宙広
    • Organizer
      Parabolic and Navier-Stokes Equations 2012
    • Place of Presentation
      バナッハ研究所(ポーランド)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 特殊な構造を持った ナヴィエ・ストークス方程式の解の一様有界性2012

    • Author(s)
      澤田 宙広
    • Organizer
      日本流体力学会年会
    • Place of Presentation
      高知大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] ナヴィエ・ストークス方程式の臨界空間での非適切性定理2012

    • Author(s)
      澤田 宙広
    • Organizer
      日本数学会秋季総合分科会 実函数論分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] スピン・コート現象の数理 ~最大正則性定理応用とニュートンポリゴンの方法~2011

    • Author(s)
      澤田宙広
    • Organizer
      神戸解析セミナー
    • Place of Presentation
      神戸大学
    • Year and Date
      2011-12-02
    • Related Report
      2012 Final Research Report
  • [Presentation] スピン・コート現象の数理~最大正則性定理応用とニュートンポリゴンの方法~2011

    • Author(s)
      澤田宙広
    • Organizer
      神戸大学理学部・神戸解析セミナー
    • Place of Presentation
      神戸大学理学部
    • Year and Date
      2011-12-02
    • Related Report
      2011 Annual Research Report

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Published: 2011-09-05   Modified: 2019-07-29  

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