On the Schrodinger equation outside strictly convex obstacles

2008/09/05 by Ivanovici, Oana
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0809.1060

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.

Related

• Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary
• Strichartz estimates without loss outside many strictly convex obstacles
• About the wave equation outside two strictly convex obstacles
• Endpoint Strichartz estimates for the Schrödinger equation on an exterior domain
• Strichartz estimates without loss outside two strictly convex obstacles