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

Oana Ivanovici (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: wave equation; Strichartz estimates; cusp type singularities

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici. Counter-examples to the Strichartz estimates for the wave equation in domains II. 2009. ⟨hal-00364946v3⟩