Research of Navier-Stokes equations in undounded domains by real analysis and the energy method
| Project/Area Number |
25400185
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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 |
Mathematical 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)
KOZONO Hideo 早稲田大学, 理工学術院, 教授 (00195728)
TANAKA Kazunaga 早稲田大学, 理工学術院, 教授 (20188288)
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| Research Collaborator |
TAKAHASHI Go 早稲田大学, 基幹理工学研究科, 大学院生
FARWIG Reinhard Darmstadt工科大学, 教授
GALDI Giovanni Paolo Pittsburgh大学, 教授
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | Navier-Stokes 方程式 / 2次元 / 定常解 / 安定性 / 対称性 / Navier-Stokes方程式 / 2次元領域 / 外部問題 / エネルギー不等式 / エネルギー法 / 解析的半群 |
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| Outline of Final Research Achievements |
For the Boussinesq equations, we established the unique existence of the solutions, and obtained the asymptotic behavior up to the second order.
Besides, for the stationary Navier-Stokes euqations on two-dimensional whole plane and exterior domains, we introduced a new assumption on the symmetry of domains, external force and the boundary value, and showed the existence of solutions which decay at infinity.
Further, under a weaker assumption on the symmetry, we showed the global asymptotic stability of the stationary solutions under arbitrary perturbations in the L2-space, together with the speed of decay measured by various norms.
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Report
(5 results)
Research Products
(10 results)
