Wave Seminar
 Date

2013725 14:30 
2013725 18:00
 Place
 Faculty of Science Building #3, Room 210

Speaker/Organizer
 Nikolay Tzvetkov (Université de CergyPontoise), Tetsu Mizumachi (Kyushu University)

 Programme
14:3016:00
Tetsu Mizumachi (Kyushu University)
Stability of line solitons for the KPII equation in R²
16:3018:00
Nikolay Tzvetkov (Université de CergyPontoise)
Invariant measures and long time behavior for the BenjaminOno equation
Abstract
（Nikolay Tzvetkov）
The KdV and the BenjaminOno equations are basic models, derived from the water waves equations for the propagation of long, small amplitude one dimensional waves. The solutions of the KdV equations, posed on the torus are known to be almost periodic in time. The long time behavior of the BenjaminOno equation, posed on the torus is much less understood. In this talk, we will present some progress on this problem. Namely, we shall construct an infinite sequence of weighted gaussian measures which are invariant by the flow of the BenjaminOno equation. These measures are supported by Sobolev spaces of increasing regularities. The "probabilistic view point" is essential in our analysis. In particular our arguments are less dependent on the particular behavior of each trajectory, compared to previous works on the subject. The talk is based on a series of joint works with Nicola Visciglia.