Counter-examples to the Strichartz estimates for the wave equation in domains II - Mathematics > Analysis of PDEsReport as inadecuate




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Abstract: We consider a smooth and bounded domain of dimension d>1 and we constructsolutions to the wave equation with Dirichlet boundary conditions whichcontradict the Strichartz estimates of the free space, at least for a subset ofthe usual range of indices. This is due to micro-local phenomena such ascaustics generated in arbitrarily small time near the boundary.



Author: Oana Ivanovici LM-Orsay

Source: https://arxiv.org/



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