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Global existence for energy critical waves in 3-D domains. (English) Zbl 1204.35119
The authors 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.

MSC:
35L71 Second-order semilinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
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