Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle

By Jason Metcalfe. 2002

58 citations recorded by the source corpus.

hhIn this paper, we show that certain local Strichartz estimates for solutions of the wave equation exterior to a convex obstacle can be extended to estimates that are global in both space and time. This extends the work that was done previously by H. Smith and C. Sogge in odd spatial dimensions. In order to prove the global estimates, we explore weighted Strichartz estimates for solutions of the wave equation when the Cauchy data and forcing term are compactly supported.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7a1e045687c331f38416cfec1c069121983c70c5

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Global Strichartz Estimates for Nontrapping Geometries: About an Article by H. Smith and C. Sogge (2002, methodology): “At the final stage of this work, I have learned that the results of this article have been obtained independently (by a slightly different method) by Jason Metcalfe [9]”
Concerning the wave equation on asymptotically Euclidean manifolds (2008, methodology): “And recently, Metcalfe and Tataru have obtained global Strichartz estimates involving small perturbations of the Minkowski metric in [24].”
Strichartz estimates for the wave equation on manifolds with boundary (2008, unknown): “We refer to [23] for the case of odd dimensions, and Burq [4] and Metcalfe [16] for the case of even dimensions.”
On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles (2008, background): “A key step in the proof of Theorem 1.4 will be to establish the following result that is implicit in [4].”