2015 Fiscal Year Final Research Report
wave equations and harmonic analysis
| Project/Area Number |
24540202
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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 |
Global analysis
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| Research Institution | Saitama University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 非線形波動方程式 / 初期値問題の適切性 / トレース定理 / ハーディの不等式 |
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| Outline of Final Research Achievements |
The aims for our research are the following three studies: (1) Well-posedness and ill-posedness results for the Cauchy problem of some nonlinear wave euations. (2) The restriction theorems for the solutions for Schrodinger equations. (3) Hardy's inequalities, especially with the critical exponents.
For those aims, our results are the followings. (1) We studied the Cauchy problem for the Dirac-klein-Gordon equation, Chern-Simons-Dirac equation and the nonlinear half wave equations. We obtained some well-posed results and ill-posed results. Especially for Chern-Simons-Dirac equation, we succeed to define the class of well-posed or Ill-posed results in Sobolev spaces. (2) We found the class of extremizers for the trace theorem on the sphere. (3) We proved the Hardy inequality holds with some condition of index and fails with others.
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| Free Research Field |
偏微分方程式
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