2015 Fiscal Year Final Research Report
Relations between properties of solutions and geometric symmetry of solutions for nonlinear wave equations
Project/Area Number |
26887017
|
Research Category |
Grant-in-Aid for Research Activity Start-up
|
Allocation Type | Single-year Grants |
Research Field |
Mathematical analysis
|
Research Institution | Shinshu University |
Principal Investigator |
OKAMOTO Mamoru 信州大学, 学術研究院工学系, 助教 (40735148)
|
Project Period (FY) |
2014-08-29 – 2016-03-31
|
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 |
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.
|
Free Research Field |
数物系科学
|