10/19/2009

Oana Ivanovici
Johns Hopkins University

Counterexamples to the Strichartz estimates for the wave equation in domains

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.