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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Global existence for energy critical waves in $ 3$-d domains


Authors: Nicolas Burq, Gilles Lebeau and Fabrice Planchon
Journal: J. Amer. Math. Soc. 21 (2008), 831-845
MSC (2000): Primary 35L05, 35L70
Published electronically: January 31, 2008
MathSciNet review: 2393429
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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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Additional Information

Nicolas Burq
Affiliation: Laboratoire de Mathématiques, Université Paris Sud, UMR 8628 du C.N.R.S., Bât 425, 91405 Orsay Cedex, France and Institut Universitaire de France
Email: Nicolas.burq@math.u-psud.fr

Gilles Lebeau
Affiliation: Laboratoire J.-A. Dieudonné, UMR 6621 du C.N.R.S, Université de Nice - Sophia Antipolis, Parc Valrose 06108 Nice Cedex 02, France and Institut Universitaire de France
Email: lebeau@math.unice.fr

Fabrice Planchon
Affiliation: Laboratoire Analyse, Géométrie & Applications, UMR 7539 du C.N.R.S, Institut Galilée, Université Paris 13, 99 avenue J.B. Clément, F-93430 Villetaneuse, France
Email: fab@math.univ-paris13.fr

DOI: http://dx.doi.org/10.1090/S0894-0347-08-00596-1
PII: S 0894-0347(08)00596-1
Keywords: Wave equation, Dirichlet boundary conditions.
Received by editor(s): July 27, 2006
Published electronically: January 31, 2008
Additional Notes: The third author was partially supported by A.N.R. grant ONDE NON LIN
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.