Strichartz-type Estimates for Wave Equation for Normally Hyperbolic Trapped Domains

Abstract

We establish a mixed-norm Strichartz type estimate for the wave equation on Riemannian manifolds $(\Omega ,g)$, for the case that $\Omega$ is the exterior of a smooth, normally hyperbolic trapped obstacle in $n$ dimensional Euclidean space, and $n$ is a positive odd integer. As for the normally hyperbolic trapped obstacles, we will some loss of derivatives for data in the local energy decay estimate. Hence the global Strichartz estimate has a derivative loss. However, we can show that the forcing term is bounded by the sum of no more than two Lebesgue $(p,q)$ mixed norms.

13 pages

References in corpus (2)

• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation
• Local smoothing for the Schrödinger equation with a prescribed loss