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Article Dans Une Revue Journal of the American Mathematical Society Année : 2008

Global existence for energy critical waves in 3-D domains

Résumé

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.

Dates et versions

hal-00102524 , version 1 (02-10-2006)

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Citer

Nicolas Burq, Gilles Lebeau, Fabrice Planchon. Global existence for energy critical waves in 3-D domains. Journal of the American Mathematical Society, 2008, 21, pp.831-845. ⟨10.1090/S0894-0347-08-00596-1⟩. ⟨hal-00102524⟩
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