Relations between properties of solutions and geometric symmetry of solutions for nonlinear wave equations

2015 Fiscal Year Final Research Report

• 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