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 domain with smooth boundary such that there exist a point on the boundary and a bicharacteristic tangent at this point and having exactly second order contact with the boundary and we construct solutions to the wave equation with Dirichlet boundary conditions which provide losses of derivatives for the Strichartz estimates, at least for a subset of the usual range of indices.

Mots clés: wave equation; Strichartz estimates

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici. Counter-examples to the Strichartz estimates for the wave equation in domains II. 2009. ⟨hal-00364946v2⟩