Counter-examples to the Strichartz estimates for the wave equation in domains II

Details Counter-examples to the Strichartz estimates for the wave equation in domains II Counter-examples to the Strichartz estimates for the wave equation in domains II

2009-02-28

arxiv.org/abs/0903.0048v3

Mathematics

Analysis of PDEs

Final version (corrected some issues in Sections 3 and 4, added some details in Section 3), 58 pages

Scientific paper

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.

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