On the Schrodinger equation outside strictly convex obstacles

Details On the Schrodinger equation outside strictly convex obstacles On the Schrodinger equation outside strictly convex obstacles

2008-09-05

arxiv.org/abs/0809.1060v3

Mathematics

Analysis of PDEs

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

Scientific paper

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.

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