Global existence for energy critical waves in 3-d domains

Burq, Nicolas; Lebeau, Gilles; Planchon, Fabrice

doi:10.1090/S0894-0347-08-00596-1

Global existence for energy critical waves in $3$-d domains
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by Nicolas Burq, Gilles Lebeau and Fabrice Planchon

J. Amer. Math. Soc. 21 (2008), 831-845

DOI: https://doi.org/10.1090/S0894-0347-08-00596-1

Published electronically: January 31, 2008

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Abstract:

We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(\Omega ) \times L^2( \Omega )$ for any smooth (compact) domain $\Omega \subset \mathbb {R}^3$. 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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