Counter-examples to the Strichartz estimates for the wave equation in domains II
arXiv:0903.0048
Abstract
We consider a smooth and bounded domain of dimension d>1 and we construct solutions to the wave equation with Dirichlet boundary conditions which contradict the Strichartz estimates of the free space, at least for a subset of the usual range of indices. This is due to micro-local phenomena such as caustics generated in arbitrarily small time near the boundary.
arXiv commentFinal version (corrected some issues in Sections 3 and 4, added some details in Section 3), 58 pages