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
DOI:
https://doi.org/10.1090/S0894-0347-08-00596-1
Published electronically:
January 31, 2008
MathSciNet review:
2393429
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
315457
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
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.