2012 Fiscal Year Final Research Report
Mathematical analysis of spin-coat
| 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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| Keywords | 偏微分方程式 / スピンコート / ナヴィエ・ストークス |
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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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