On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles

By K. Hidano, Jason Metcalfe, Hart F. Smith, Christopher D. Sogge, Yi Zhou. 2008

73 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5919647c7339bb825b2700876c92d065fc7951a4

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Decay estimates for variable coefficient wave equations in exterior domains (2008, methodology): “Local-in-time estimates were shown in [19] for convex obstacles, and using these estimates, global estimates were constructed in [20] for n odd and [3] and [14] for general n.”
Strichartz estimates for the wave equation on manifolds with boundary (2008, background): “an obtain global in time Strichartz estimates under a nontrapping assumption. We refer to [24] for the case of odd dimensions, and Burq [4] and Metcalfe [17] for the case of even dimensions. See also [11]. For a manifold with strictly geodesically-concave boundary, the Melrose-Taylor parametrix yiel”