For more information about this meeting, contact Mary Anne Raymond.

Title: | : Large time blow up for a perturbation of the cubic Szegő equation |

Seminar: | Complex Fluids Seminar |

Speaker: | Haiyan Xu, University Paris-Sud 11 |

Abstract: |

I am going to discuss a pertubed cubic Szegő equation
i u_t = Pi (|u|^2u) + α (u|1)
on the circle, where Pi is the Szegő projector on non-negative frequencies. This equation with α=0 was recently introduced as a toy model for totally non dispersive evolution equations by P. Gerard (Paris-Sud University, Orsay, France) and S. Grellier (University of Orleans, France). It is globally well-posed with a Lax pair structure for any real number α. Given initial data in a special subset of rational functions, the solutions stay in a relatively compact subset of trajectories for α<0. While for α> 0, there exist trajectories on which high Sobolev norms exponentially grow with time. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 08 / 18 / 2014 |

Time: | 10:00am - 11:30am |