On asymptotic stability in energy space of ground states of NLS in 2D

TL;DR

This paper extends the understanding of the asymptotic stability of ground states in 2D nonlinear Schrödinger equations by establishing dispersive estimates and adapting stability results previously known in other dimensions.

Contribution

It provides dispersive and smoothing estimates for linearized solutions at ground states in 2D and extends asymptotic stability results to this dimension.

Findings

Dispersive estimates for linearized solutions in 2D

Extension of asymptotic stability results to 2D NLS

Adaptation of techniques from higher dimensions

Abstract

We transpose work by K.Yajima and by T.Mizumachi to prove dispersive and smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 2D. As an application we extend to dimension 2D a result on asymptotic stability of ground states of NLS proved in the literature for all dimensions different from 2.