Real analytic research on the Navier-Stokes equations on exterior domains with external force
Project/Area Number |
17K05339
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Mathematical analysis
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Research Institution | Waseda University |
Principal Investigator |
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Project Period (FY) |
2017-04-01 – 2023-03-31
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Project Status |
Completed (Fiscal Year 2022)
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Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | Navier-Stokes方程式 / 外部領域 / 安定性 / Lorentz空間 / 実補間 / 対称性 / 時間周期解 / 概周期解 / 補間理論 / Navier-Stokes / 非有界領域 / ancient solution / 周期解 / Ap-weight / 特異積分 / 2次元h非有界領域 / Muchkenhoupuptクラス / 定常解 / エネルギー不等式 / 解の一意性 / 函数空間 / 解析学 / 関数方程式論 / 実関数論 |
Outline of Final Research Achievements |
The author investigated Navier-Stokes equations, which describe motion of incompressible fluids, in 2-dimensional unbouded domains. (In particular exterior Gdomains.) The author first considered stationary problem in exterior domains. No genaral condition was obtained for the existence of solutions which decay at infinity. The author showed the unique existence of weak solutions satisfying energy inequality under the assumption under newly introduced symmetry assumptions on domains, external forces and the boundary conditions. The author next considered on the whole plane in the case where external forces depends on time. Under the aforementioned symmetry condition on the external forces, the author showed the unique existence and stability of small solutions. in oreder to overcome the weak decay in 2-dimension, we employed the weighted Lorentz spaces.
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Academic Significance and Societal Importance of the Research Achievements |
Navier-Stokes 方程式は航空機、船舶、鉄道車両、自動車盗の製造に重要な役割を果たす。本研究は具体的な問題に直接かかわっていないが、Navier-Stokes方程式に新たな知見を与え, その研究の進展にきよするものである。
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Report
(7 results)
Research Products
(3 results)