11/13/2006

Nicolas Burq
Paris 11

Global existence for energy critical waves in 3-d domains

We prove that the quintic (critical) defocussing wave equation with Dirichlet boundary conditions in a 3-d bounded domain is globally well posed in energy space. The main ingredient of the proof is an (optimal) Strichartz inequality derived from some recent spectral projector estimates by Smith and Sogge and a precise study of the boundary value problem.