Global existence for energy critical waves in 3-D domains

Burq, Nicolas; Lebeau, Gilles; Planchon, Fabrice

Global existence for energy critical waves in 3-D domains

Authors

Burq, Nicolas

Lebeau, Gilles

Planchon, Fabrice

Description

We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(Ω) \times L^2(Ω)$ for any smooth (compact) domain $Ω\subset \mathbb{R}^3$. 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.
15 pages, 2 figures