Abstract

We prove that the defocusing quintic wave equation, with Neumann boundary conditions, is globally well-posed on $H^1_N(\Omega) \times L^2( \Omega)$ for any smooth (compact) domain $\Omega \subset {\Bbb R}^3$. The proof relies on one hand on $L^p$ estimates for the spectral projector, and on the other hand on a precise analysis of the boundary value problem, which turns out to be much more delicate than in the case of Dirichlet boundary conditions.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1715-1742
Launched on MUSE
2009-12-05
Open Access
No
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