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

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 Schrödinger 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.

References in corpus (4)

• Selection of the ground state for nonlinear Schroedinger equations
• Dispersive estimates for Schroedinger operators in dimension two
• On asymptotic stability in energy space of ground states for Nonlinear Schrödinger equations
• On the asymptotic stability of bound states in 2D cubic Schroedinger equation

Cited by in corpus (3)

• On eigenfunction expansion of solutions to the Hamilton equations
• On orbital instability of spectrally stable vortices of the NLS in the plane
• Dispersive estimates for matrix Schrödinger operators in dimension two