English

$H^1$ 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 Σ\Sigma scatter in H1H^1. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumifrom L2L^2 to H1H^1.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 Σ\Sigma.

Keywords

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}
}
R2 v1 2026-06-24T07:38:54.225Z