Preprints, Working Papers, ... Year : 2021

$H^1$ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in $\Sigma$

N. Burq
  • Function : Author
V. Georgiev
  • Function : Author
N. Visciglia
  • Function : Author

Abstract

We consider short-range mass-subcritical nonlinear Schr\"odinger equations and we show that the corresponding solutions with initial data in $\Sigma$ scatter in $H^1$. Hence we up-grade the classical scattering result proved by Yajima and Tsutsumifrom $L^2$ to $H^1$.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 $\Sigma$.

Dates and versions

ensl-04829767 , version 1 (10-12-2024)

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Cite

N. Burq, V. Georgiev, N. Tzvetkov, N. Visciglia. $H^1$ scattering for mass-subcritical NLS with short-range nonlinearity and initial data in $\Sigma$. 2024. ⟨ensl-04829767⟩
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