Global existence for energy critical waves in 3-d domains : Neumann boundary conditions

Details Global existence for energy critical waves in 3-d domains : Neumann boundary conditions Global existence for energy critical waves in 3-d domains : Neumann boundary conditions

2007-11-02

arxiv.org/abs/0711.0275v1

Mathematics

Analysis of PDEs

21 pages, 1 figure

Scientific paper

We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally wellposed on $H^1_N(\Omega) \times L^2(\Omega)$ for any smooth (compact) domain $\Omega \subset \mathbb{R}^3$. 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.

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