2012 Fiscal Year Final Research Report
An Investigation of symmetries and structure of solutions for nonlinear dispersive equation
| Project/Area Number |
21684003
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (A)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
TAKAOKA Hideo 北海道大学, 大学院・理学研究院, 教授 (10322794)
|
|---|
| Project Period (FY) |
2009 – 2012
|
| Keywords | 非線形分散型 / 適切性 / 初期値問題 |
|---|
| Research Abstract |
In this study, I have developed the local and global well-posedness for the initial value problem related to a class of nonlinear dispersive equations, such as the KdV equations and the nonlinear Schrodinger equations. I investigated the propagation of singularities of solutions using Fourier analysis, and obtained the local in time unique existence of solutions to the modified KdV equation.
Moreover, I proved the global energy estimate for the nonlinear Schrodinger equations, and proved global in time unique existence of solutions and invariance of the associated Gibbs measure to the derivative nonlinear Schrodinger equation.
|
