2012 Fiscal Year Final Research Report
Study on the Navier-Stokes equations on unbounded domains by way of real analysis
| Project/Area Number |
21540202
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Waseda University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
SHIBATA Yoshihiro 早稲田大学, 理工学術院, 教授 (50114088)
TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 関数方程式 / 偏微分方程式論 |
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| Research Abstract |
This research is concerned with the Navier-Stokes equations on either the whole plane or two-dimensional exterior domains. It was shown that, if there exists a small stationary external force with strong symmetry, the equation has a small stationary solution decaying rapidly at infinity. It was also shown that, if the stationary solution above is sufficiently small, it is stable under initial perturbation without restriction on the size. The Navier-Stokes equaions in an infinite layer is also studied. It is shown that, if the equation is treated in the Besov spaces, nontrivial solutions with no external forces exist if p is infinite, and that these solutions correspond to the Poiseuille flows.
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