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^sup 1^^sub N^ (Ω) × L^sup 2^(Ω) for any smooth (compact) domain Ω ⊂ R^sup 3^. The proof relies on one hand on L^sup 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. [PUBLICATION ABSTRACT]