Mathematical analysis of dispersion and anisotropy in rotating fluids
| Project/Area Number |
25887005
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
TAKADA RYO 東北大学, 理学(系)研究科(研究院), 助教 (50713236)
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| Project Period (FY) |
2013-08-30 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 偏微分方程式 / 流体力学 / 非圧縮性流体 / 回転流体 / Navier-Stokes 方程式 / Euler 方程式 / Coriolis 力 / 分散型評価 / 温度成層 / Boussinesq 方程式 / 非圧縮性 Euler 方程式 / 非圧縮性 Navier-Stokes 方程式 / Strichartz 評価 |
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| Outline of Final Research Achievements |
This research project aims to analyze nonlinear partial differential equations describing the motion of incompressible rotating fluids mathematically. We established dispersive and space-time estimates for the linear propagator generated by the Coriolis force. As an application, we proved the long time existence of solutions to the initial value problem for the incompressible rotating Euler equations. It is expected that our results and techniques obtained in this research can be applied to the study of the rotating shallow water equations and the primitive equations.
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Report
(3 results)
Research Products
(27 results)
