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