Scattering below ground state of focusing fractional nonlinear Schrödinger equation with radial data

Chenmin Sun; Hua Wang; Xiaohua Yao; Jiqiang Zheng

doi:10.3934/dcds.2018091

Article Contents

2018, Volume 38, Issue 4: 2207-2228. Doi: 10.3934/dcds.2018091

This issue Previous Article New periodic orbits in the planar equal-mass three-body problem Next Article

Scattering below ground state of focusing fractional nonlinear Schrödinger equation with radial data

1.
Université Côte d'Azur, LJAD, 06100, France
2.
Department of Mathematics and Hubei Province Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan 430079, China
3.
Université Côte d'Azur, LJAD, 06100, France

* Corresponding author: Hua Wang
* Corresponding author: Hua Wang

Received: May 31, 2017

Revised: September 30, 2017

Published: June 2018

The first and last authors are financed by ERC project SCAPDE, the second author is supported by NSF grant 11101172, 11371158 and 11571131, and the third author is supported by NSF grant 11371158 and 11771165

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Abstract

The aim of this paper is to adapt the strategy in [8] [ 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. The main ingredient is to apply the fractional virial identity proved in [3] [ 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.

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Mathematics Subject Classification: Primary: 35P25, 35Q55; Secondary: 47J35.

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