Counter-examples to the Strichartz estimates for the wave equation in domains II
Analysis of PDEs
2010-02-08 v3
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.
Keywords
Cite
@article{arxiv.0903.0048,
title = {Counter-examples to the Strichartz estimates for the wave equation in domains II},
author = {Oana Ivanovici},
journal= {arXiv preprint arXiv:0903.0048},
year = {2010}
}
Comments
Final version (corrected some issues in Sections 3 and 4, added some details in Section 3), 58 pages