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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:300

Article

Ivanovici, Oana¹  Lebeau, Gilles²  Planchon, Fabrice³ 

[1] Sorbonne Univ, LJLL, CNRS, F-75005 Paris, France

[2] Univ Cote Azur, Lab JAD, CNRS, Nice, France

[3] Sorbonne Univ, IMJ PRG, CNRS, F-75005 Paris, France

关键词: Dispersive estimates;    Wave equation;    Dirichlet boundary condition;   

DOI  :  10.1016/j.jde.2021.08.011

来源: Elsevier

【 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.

【 授权许可】

Free