2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141295We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally wellposed on $H^1_N(Ω) \times L^2(Ω)$ for any smooth (compact) domain $Ω\subset \mathbb{R}^3$. The proof relies on one hand on $L^p$ estimates for the spectral projector by Smith and Sogge, 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.21 pages, 1 figureAnalysis of PDEstext