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

2020/08/31 by Oana Ivanovici, Gilles Lebeau, Fabrice Planchon · 1 citation
Mathematics · #math.AP #msc:35A17 #msc:35B45 #msc:35L10 #msc:35L20 #msc:35R01

paper · pdf · doi:10.5802/jep.168

published as Journal de l'École polytechnique -- Mathématiques, Tome 8 (2021), pp. 1133-1157 · 23 pages, 1 figure

arxiv created 2021/06/10 · arxiv updated 2021/06/14

Abstract

We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family of counterexamples is now built on the parametrix construction from our earlier work. Interestingly enough, it is sharp in at least some regions of phase space.

Cited by

• Counterexamples to Strichartz estimates and gallery waves for the irrotational compressible Euler equation in a vacuum setting