Counterexamples to the Strichartz inequalities for the wave equation in domains II

  title={Counterexamples to the Strichartz inequalities for the wave equation in domains II},
  author={Oana Ivanovici},
In this paper we consider a smooth and bounded domain Ω ⊂ Rd of dimension d ≥ 2 with smooth boundary ∂Ω and we construct sequences of solutions to the wave equation with Dirichlet boundary conditions which contradict the Strichartz estimates of the free space, providing losses of derivatives 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. The result we obtain here is a… CONTINUE READING

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