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 H1-critical (quintic) Schrodinger equation and scattering for the sub-critical Schrodinger equation in 3D.
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