GLOBAL EXISTENCE FOR ENERGY CRITICAL WAVES IN 3-D DOMAINS: NEUMANN BOUNDARY CONDITIONS

摘要

We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally well-posed on H-N(1)(Omega) x L-2(Omega) for any smooth (compact) domain Omega subset of R-3. The proof relies on one hand on L-p estimates for the spectral projector, and on the other hand on a precise analysis of the boundary value problem, which turns out to be much more delicate than in the case of Dirichlet boundary conditions.