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Global existence for energy critical waves in  -d domains |
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| Authors: | Nicolas Burq Gilles Lebeau Fabrice Planchon |
| Institution: | Laboratoire de Mathématiques, Université Paris Sud, UMR 8628 du C.N.R.S., Bât 425, 91405 Orsay Cedex, France and Institut Universitaire de France ; 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 ; 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 |
| Abstract: | We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on  for any smooth (compact) domain  . The main ingredient in the proof is an  spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem. |
| Keywords: | Wave equation Dirichlet boundary conditions |
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