Global existence for energy critical waves in 3-D domains

Nicolas Burq; Gilles Lebeau; Fabrice Planchon

Global existence for energy critical waves in 3-D domains

Analysis of PDEs 2007-05-23 v1

Authors: Nicolas Burq , Gilles Lebeau , Fabrice Planchon

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.

Keywords

wave equation global well-posedness energy critical dirichlet boundary spectral projector estimate

Cite

@article{arxiv.math/0607631,
  title  = {Global existence for energy critical waves in 3-D domains},
  author = {Nicolas Burq and Gilles Lebeau and Fabrice Planchon},
  journal= {arXiv preprint arXiv:math/0607631},
  year   = {2007}
}

Comments

15 pages, 2 figures

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