2011 Fiscal Year Final Research Report
Mathematical analysis of an incompressible viscous fluid in an infinite layer by methods of real analysis
| Project/Area Number |
20740083
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Kisarazu National College of Technology |
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Principal Investigator |
ABE Takayuki 木更津工業高等専門学校, 基礎学系, 准教授 (70396274)
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| Project Period (FY) |
2008 – 2011
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| Keywords | Navier-Stokes方程式 / Stokes方程式 / レゾルベント評価 / 解析的半群 / 自由境界問題 / Besov空間 / 斉次Besov空間 / Maximal regularity |
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| Research Abstract |
We analyze a resolvent problem of the Stokes equation in an infinite layer and prove that the Stokes operator generates an analytic semigroup on Holder and Besov spaces. As an application, we prove a stability of some special solutions in Besov spaces. Moreover, we prove maximal regularity for the Stokes equation by operator-valued Fourier multiplier theorem, and we prove unique existence of a local in time solution to free boundary problems of the Navier-Stokes equation.
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