11/22/2006

Fabrice Planchon
Paris 13

Energy critical waves on a domain: non concentration arguments vs
boundary conditions

In a joint work with N. Burq and G. Lebeau we proved global existence for the quintic defocusing wave equation on a domain, with Dirichlet boundary condition. The local existence part relies on highly non trivial dispersive estimates; in this talk we will focus on the second part, which is to extend such local solutions to global ones. The boundary interferes with Morawetz-like estimates and requires additional a priori estimates on the trace. We will also outline the strategy toward the Neumann problem.