|SPEAKER||Yoshio Tsutsumi 教授（京都大學）|
|TITLE||Quasi-Invariant Gaussian Measures for NLS with Third Order Dispersion|
Invariant measures for nonlinear evolution equations have been attracted the attention of many researchers. Especially, the Gibbs measure for the Hamiltonian system is natural and important from both mathematical and physical points of view. However, the support of the Gibbs measure is determined by the Hamiltonian of the system in question and it is often a weak function space. Therefore, the Gibbs measure does not capture smooth solutions such as finite energy solutions.
Recently, Tzvetkov showed the quasi-invariant property of Gaussian measures with support including smooth solutions for some nonlinear dispersive equations instead of the invariant property. It is very interesting, because the quasi-invariance might be able to replace the role of invariance. In this talk, I will talk about the quasi-invariance of certain Gaussian measures for NLS with third order dispersion. This is a joint work with Nikolay Tzvetkov (University of Cergy-Pontoise) and Tadahiro Oh (University of Edinburgh).