# Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data

## TL;DR

This paper extends the scattering theory for 3D focusing cubic fractional Schrödinger equations with radial data by adapting existing strategies and employing a fractional virial identity to prevent mass concentration.

## Contribution

It introduces a method to prove scattering below the ground state for certain focusing fractional NLS using a fractional virial identity, adapting previous approaches.

## Key findings

- Proved scattering for radial solutions below the ground state.
- Applied fractional virial identity to exclude mass concentration.
- Extended scattering results to fractional Schrödinger equations.

## Abstract

The aim of this note is to adapt the strategy in [4][See,B.Dodson, J.Murphy, a new proof of scattering below the ground state for the 3D radial focusing cubic NLS, arXiv:1611.04195 ] to prove the scattering of radial solutions below sharp threshold for certain focusing fractional NLS with cubic nonlinearity. The main ingredient is to apply the fractional virial identity proved in [11][See,T.Boulenger, D.Himmelsbach,E.Lenzmann, Blow up for fractional NLS,J.Func.Anal,271(2016),2569-2603] to exclude the concentration of mass near the origin.