| Project/Area Number |
23840016
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Gifu University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| 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)
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| 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 |
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| 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.
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