On the Schrodinger equation outside strictly convex obstacles

Oana Ivanovici (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Mots clés: Schrodinger equation; Strichartz inequalities

Domaines: Equations aux dérivées partielles [math.AP]

Oana Ivanovici. On the Schrodinger equation outside strictly convex obstacles. 2008. ⟨hal-00319146v3⟩