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.