2016 Fiscal Year Final Research Report
Well-posedness and ill-posedness for the nonlinear partial differential equations
| Project/Area Number |
25800069
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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 |
Basic analysis
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| Research Institution | Tohoku University (2016)
Osaka City University (2015)
Chuo University (2013-2014) |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 偏微分方程式 / 初期値問題 / 適切性および非適切性 / ベゾフ空間 |
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| Outline of Final Research Achievements |
This work is concerned with revealing and understanding the optimal initial condition for some nonlinear partial differential equations such as Navier-Stokes equations and Schrodinger equations. We studied the Navier-Stokes equations in the spaces of functions which have the bounded mean oscillation property, and also gave some initial condition for the equations with the Coriolis force. As to Schrodinger equations, we proved ill-posedness with quadratic non-linearity. It is also proved for the Burgers equation with the critical dissipation that small global solution tends to the Poisson kernel.
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| Free Research Field |
偏微分方程式論
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