Relations between properties of solutions and geometric symmetry of solutions for nonlinear wave equations
| Project/Area Number |
26887017
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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 | Shinshu University |
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Principal Investigator |
OKAMOTO Mamoru 信州大学, 学術研究院工学系, 助教 (40735148)
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非線形波動方程式 / 初期値問題の適切性 / フーリエ制限ノルム法 / 解の散乱 / チャーン・サイモンズ・ディラック方程式 / ４階シュレディンガー方程式 / Chern-Simons-Dirac方程式 |
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| Outline of Final Research Achievements |
The research results are as follows. (1) We proved the well-posedness and ill-posedness of the Cauchy problem for the one dimensional Chern-Simons-Dirac system. We completely determined the range, which is not convex, of Sobolev regularity to be well-posed. (2) We proved the global well-posedness and scattering for the fourth order nonlinear Schrodinger equation. (3) We obtain the well-posedness and ill-posedness results of the Cauchy problem for the generalized Thirring model.
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Report
(3 results)
Research Products
(17 results)
