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

TL;DR

This paper presents new counterexamples that demonstrate stricter limitations on Strichartz estimates for the wave equation on a 2D convex domain, refining previous understanding and showing sharpness in certain phase space regions.

Contribution

The authors construct a new family of counterexamples using parametrix methods, improving the known restrictions on Strichartz estimates for the wave equation in 2D convex domains.

Findings

Strichartz estimates are more restricted than previously known in certain cases.

The new counterexamples are sharp in some phase space regions.

The construction builds on earlier parametrix techniques.

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.