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Article Dans Une Revue Journal of Differential Equations Année : 2021

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

Résumé

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.

Dates et versions

hal-02938058 , version 1 (14-09-2020)

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Oana Ivanovici, Gilles Lebeau, Fabrice Planchon. Strichartz estimates for the wave equation on a 2d model convex domain. Journal of Differential Equations, 2021, 300, pp.830--880. ⟨10.1016/j.jde.2021.08.011⟩. ⟨hal-02938058⟩
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