On 2D NLS on non-trapping exterior domains

Abstract

Global existence and scattering for the nonlinear defocusing Schrödinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic. For such nonlinearities, we also prove scattering for a class of so-called almost star-shaped obstacles.

arXiv commentfixed typos and updated references, to appear in Revista Matemática Iberoamericana

References in corpus (2)

• Quintic NLS in the exterior of a strictly convex obstacle
• Asymptotics of the critical non-linear wave equation for a class of non star-shaped obstacles