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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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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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 / 半相対論方程式 / チャーン サイモンズ方程式 / 適切性 / 非適切性 / Chern-Simons-Dirac方程式 / 非線形シュレディンガー方程式 / Hardy の不等式 / Lorentz 空間 / 再配分関数 / シュレディンガー方程式 |
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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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Report
(5 results)
Research Products
(28 results)
