On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles

Hidano, Kunio; Metcalfe, Jason; Smith, Hart; Sogge, Christopher; Zhou, Yi

doi:10.1090/S0002-9947-09-05053-3

On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles
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by Kunio Hidano, Jason Metcalfe, Hart F. Smith, Christopher D. Sogge and Yi Zhou PDF

Trans. Amer. Math. Soc. 362 (2010), 2789-2809 Request permission

Abstract:

We establish the Strauss conjecture concerning small-data global existence for nonlinear wave equations, in the setting of exterior domains to compact obstacles, for space dimensions $n=3$ and $4$. The obstacle is assumed to be nontrapping, and the solution is assumed to satisfy either Dirichlet or Neumann conditions along the boundary of the obstacle. The key step in the proof is establishing certain “abstract Strichartz estimates” for the linear wave equation on exterior domains.

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