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

[摘要] We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained earlier on a 2d convex model domain. This follows from taking full advantage of the space-time localization of caustics in the parametrix, 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-05

[关键词] Dispersive estimates;Wave equation;Dirichlet boundary condition