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

• Autores: Nicolas Burq, Gilles Lebeau, Fabrice Planchon
• Localización: Journal of the American Mathematical Society, ISSN 0894-0347, Vol. 21, Nº 3, 2008, págs. 831-846
• Idioma: inglés
• DOI: 10.1090/s0894-0347-08-00596-1
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• Resumen

  • 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.