Home Contact Chinese CAS
 Location: Home > Research > Colloquia & Seminars

Large time blow up for a perturbation of the cubic Szeg\H{o} equation
【2013.7.26 4:00-5:00pm,C510】

Date:03-12-2013　Page Views:
 Text Size: A A A

2013-7-24

Colloquia & Seminars

 Speaker Dr. Xu Haiyan（University of Paris 11） Title Large time blow up for a perturbation of the cubic Szeg\H{o} equation Time 2013.7.26 4:00-5:00pm Venue C510 Abstract We consider the following Hamiltonian equation on a special manifold of rational functions, $i\p_tu=\Pi(|u|^2u)+\al (u|1),\ \al\in\R,$ where $\Pi$ denotes the Szeg\H{o} projector on the Hardy space of the circle $\SS^1$. The equation with $\al=0$ was first introduced as a toy model for totally non dispersive evolution equations by P. Gerard (Paris-Sud University, France) and S. Grellier (University of Orleans, France). This equation admits a Lax pair structure due to the Hankel operator. We establish the following properties for this equation. For $\al<0$, any compact subset of initial data leads to a relatively compact subset of trajectories. For $\al>0$, there exist trajectories on which high Sobolev norms exponentially grow with time. Affiliation

 [ Close ]  [ Top ]