Analysis of concentration phenomena for nonlinear wave and dispersive equations
Description: The well-posedness of the initial value problem is the most fundamental problem in the field of nonlinear evolution equations. The well-posedness is a concept consisting of three properties: existence of solution, uniqueness and continuous dependence of solutions on initial data. It heavily depends on the sturacture of each nonlinear evolution equation when its initial value problem is well-posed, which is very attractive. The study of the structure for each important equation has a great significance, since it is extremely difficult to construct the general theory applicable to various nonlinear evolution equations. In this research, we study the well-posedness of the initial value problem for the nonlinear Schroedinger equation with Ramman scattering term and the kinetic derivative nonlinear Schroedinger equation. We have showed that the well-posedness depends on the regularity of function spaces to which solutions belong.
Amount: ¥17,680,000
Funding type: research
Funder scheme: Grant-in-Aid for Scientific Research (B)
Start date: 2017-04-01
End date: 2022-03-31
Investigator: Yoshio Tsutsumi
Institution: Kyoto University
Funded outputs count: 36
Funder award ID: 17H02853
OpenAlex ID: G6989481663