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Global existence for energy critical waves in 3-D domains

Nicolas Burq·Gilles Lebeau·Fabrice Planchon
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Abstract

We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(Ω) \times L^2(Ω)$ for any smooth (compact) domain $Ω\subset \mathbb{R}^3$. The main ingredient in the proof is an $L^5$ spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem.

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Nicolas Burq, Gilles Lebeau, Fabrice Planchon. 2006-07-25. Global existence for energy critical waves in 3-D domains. https://arxiv.org/abs/math/0607631

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