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arXiv · 0711.0275

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

N. Burq·F. Planchon
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Abstract

We 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.

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N. Burq, F. Planchon. 2007-11-02. Global existence for energy critical waves in 3-d domains : Neumann boundary conditions. https://arxiv.org/abs/0711.0275

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