Vol. 3, No. 3, 2010

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On the Schrödinger equation outside strictly convex obstacles

Oana Ivanovici

Vol. 3 (2010), No. 3, 261–293
Abstract

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 Schrödinger equation in three dimensions.

Keywords
Schrödinger equation, Strichartz estimates, exterior domain
Mathematical Subject Classification 2000
Primary: 35Q55, 37K05, 37K50