Global existence for energy critical waves in 3-D domains

Abstract

We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H_0^1(\Omega )\times L^2(\Omega )$ for any smooth (compact) domain $\Omega \subset {\mathbb{R}}^3$. The main ingredient in the proof is an $L^5$ spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem.

15 pages, 2 figures