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

Metcalfe, Jason

doi:10.1090/S0002-9947-04-03667-0

Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle
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by Jason L. Metcalfe

Trans. Amer. Math. Soc. 356 (2004), 4839-4855

DOI: https://doi.org/10.1090/S0002-9947-04-03667-0

Published electronically: June 25, 2004

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Abstract:

In 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.

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