2016 Fiscal Year Final Research Report
Analysis on the asymptotic phase behavior of the solution to partial differential equations in fluid mechanics
| Project/Area Number |
25800070
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Hirosaki University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | ナビエ・ストークス方程式 / エネルギー減衰 / 漸近展開 / 時間周期解 / 重み付きハーディー空間 / 安定性 |
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| Outline of Final Research Achievements |
On the asymptotic behavior of the solution of the Navier-Stokes equations in the half space, we obtain the lower bound of the energy decay of the solution and its spectral concentration. Separating on tangential and vertical components of the initial data, we see that the lower frequency part of the tangential components much affects the lower bound of the energy decay.
We construct a strong solution in the weighted Hardy space and obtained the higher order asymptotic expansion under the moment condition on initial data.
Under the general flux condition on the boundary, we clarified the condition for the stability of large stationary solutions in a bounded domain.
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| Free Research Field |
偏微分方程式
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