Thomas Duyckaerts (University Paris 13), PDE Mini-School

Title:  Dynamics of the energy critical wave equations

Abstract:  These lectures concern the energy-critical focusing nonlinear wave equation. It is conjectured that any solution of this equation that is bounded in the energy space is asymptotically the sum of a finite number of decoupled solitons and a radiation term. My goal is to prove this conjecture for radial solutions in space dimension 3 and to give partial results in the general case.

This is based on joint works with Hao Jia, Carlos Kenig and Frank Merle.

The lectures will start at an elementary level and will be accessible to non-specialist.