On the Schrodinger equation outside strictly convex obstacles

Abstract

We prove sharp Strichartz estimates for the semi-classical Schrodinger equation on a compact manifold with smooth, strictly geodesically concave boundary. We deduce sharp (classical) Strichartz estimates for the Schrodinger equation outside a strictly convex obstacle, local existence for the H^1-critical (quintic) Schrodinger equation and scattering for the sub-critical Schrodinger equation in 3D.

Corrections (per the referee's suggestions) were made in Section 3 and in Section 4.2, 42 pages