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arXiv · 2008.03598

Strichartz estimates for the wave equation on a 2d model convex domain

Oana Ivanovici·Gilles Lebeau·Fabrice Planchon
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Abstract

We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix we obtain, despite their number increasing like the inverse square root of the distance from the source to the boundary. As a consequence, we improve known Strichartz estimates for the wave equation. Several improvements on our previous parametrix construction are obtained along the way and are of independent interest for further applications.

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Oana Ivanovici, Gilles Lebeau, Fabrice Planchon. 2020-08-08. Strichartz estimates for the wave equation on a 2d model convex domain. https://doi.org/10.1016/j.jde.2021.08.011

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