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

Oana Ivanovici (1) , Gilles Lebeau (2) , Fabrice Planchon (3)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

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.

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici, Gilles Lebeau, Fabrice Planchon. New counterexamples to Strichartz estimates for the wave equation on a 2d model convex domain. Journal de l'École polytechnique — Mathématiques, 2021, 8, pp.1133--1157. ⟨10.5802/jep.168⟩. ⟨hal-02938051⟩