Scattering for solutions of NLS in the exterior of a 2d star--shaped obstacle

TL;DR

This paper proves that solutions to a defocusing nonlinear Schrödinger equation in 2D outside a star-shaped obstacle scatter in the energy space, extending understanding of wave behavior in complex geometries.

Contribution

It establishes scattering results for 2D NLS in exterior star-shaped domains with defocusing quintic or higher nonlinearities, a novel geometric setting.

Findings

Solutions scatter in the energy space

Results apply to nonlinearities growing at least as the quintic power

Extends scattering theory to exterior star-shaped obstacles

Abstract

We prove that solutions to non-linear Schr\"odinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non-linear potential is defocusing and grows at least as the quintic power.