Counterexamples to the Strichartz estimates for the wave equation in domains

Counterexamples to the Strichartz estimates for the wave equation in domains

-
Oana Ivanovici, Johns Hopkins University
Fine Hall 110

We prove that the Strichartz estimates for the wave equation inside a strictly convex domain $\Omega$ of dimension $2$ suffer losses when compared to the usual case $\mathbb{R}2$, (at least for a subset of the usual range of indices) and this is due to microlocal phenomena such as caustics generated in arbitrariIly small time near the boundary.