$H^1$ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in $\Sigma$
Analysis of PDEs
2021-11-16 v1 Mathematical Physics
math.MP
Abstract
We consider short-range mass-subcritical nonlinear Schr\"odinger equations and we show that the corresponding solutions with initial data in scatter in . Hence we up-grade the classical scattering result proved by Yajima and Tsutsumifrom to .We also provide some partial results concerning the scattering of the first order moments, as well as a short proof via lens transform of a classical result due to Tsutsumi and Cazenave-Weissler on the scattering in .
Cite
@article{arxiv.2111.07802,
title = {$H^1$ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in $\Sigma$},
author = {N. Burq and V. Georgiev and N. Tzvetkov and N. Visciglia},
journal= {arXiv preprint arXiv:2111.07802},
year = {2021}
}