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Article Dans Une Revue American Journal of Mathematics Année : 2009

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

N. Burq

Résumé

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.

Dates et versions

hal-00449546 , version 1 (22-01-2010)

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N. Burq, F. Planchon. Global existence for energy critical waves in 3-d domains : Neumann boundary conditions. American Journal of Mathematics, 2009, 131 (6), pp.1715--1742. ⟨hal-00449546⟩
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