Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
In this paper we consider a smooth and bounded domain \Omega\subset\mathbb{R}^d of dimension d\geq 2 with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of …