2014 Fiscal Year Final Research Report
Mathematical analysis of decay structure of a viscous incompressible fluid arising from motions of obstacles
| Project/Area Number |
24540169
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Keywords | 非圧縮粘性流 / 減衰構造 / Navier-Stokes方程式 / Stokes流 / Oseen流 / 外部領域 / 漸近展開 / 基本解 |
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| Outline of Final Research Achievements |
Suppose that a rigid obstacle is moving in a viscous incompressible fluid, where the space dimension is either 2 or 3. Then we have analyzed how the motion of the rigid body affects the spatial/temporal decay structure of the fluid. In particular, the large time behavior of the Oseen semigroup for translating body case and asymptotic expansion at space infinity of steady linearized flow for rotating body case are provided. Furthermore, for fluid-structure interaction problem in 3D, we have shown the boundary controllability of the self-propelled motion of a rigid body, whose translation and rotation are prescribed but not very large. Besides the results mentioned above, the stability of small time-dependent flow as well as steady flow has been proved in a 2D aperture domain and in 3D whole space.
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| Free Research Field |
函数方程式論
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