On the Schrödinger equation outside strictly convex obstacles

Abstract

We prove sharp Strichartz estimates for the semiclassical Schrodinger equation on a compact Riemannian manifold with a smooth, strictly geodesically concave boundary. We deduce classical Strichartz estimates for the Schrodinger equation outside a strictly convex obstacle, local existence for the H1-critical (quintic) Schrodinger equation, and scattering for the subcritical Schrodinger equation in three dimensions.