On the Schrödinger equation outside strictly convex obstacles
On the Schrödinger equation outside strictly convex obstacles
We prove sharp Strichartz estimates for the semiclassical Schrödinger equation on a compact Riemannian manifold with a smooth, strictly geodesically concave boundary.We deduce classical Strichartz estimates for the Schrödinger equation outside a strictly convex obstacle, local existence for the H 1 -critical (quintic) Schrödinger equation, and scattering for the subcritical …