杨建伟,北理工

Consider the linear wave equations with a potential outside a compact set with a non-trapping boundary condition. Assuming that the potential satisfies an appropriate decreasing condition and that zero is not an eigenvlue or a resonance, we prove that the solution of the wave equation projected to the subspace associated to the continuous spectrum of the Schr?dinger operator satisfies global Strichartz estimates. Our method is based on the local Strichartz estimate in exterior domains without potential, a result going back to Smith-Sogge, and the local energy decay which is obtained from a uniform resolvent estimate. This work is joint with Thomas Duyckaerts.