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Global existence for energy critical waves in 3-D domains: Neumann boundary conditions. (English) Zbl 1184.35210
The authors prove global well posedness of the initial-boundary value problem to the equation \(u_{tt}-\Delta u+u^5=0\) with the Neumann boundary conditions on \(H^1_N(\Omega)\times L^2(\Omega)\), where \(\Omega \) is a smooth bounded domain in \(R^3\). Combining trace estimates and nonconcentration arguments they extend local to global existence of the solution for arbitrary finite energy data.

35L71 Second-order semilinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B33 Critical exponents in context of PDEs
35B60 Continuation and prolongation of solutions to PDEs
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