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arXiv · 1702.03148

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

Chenmin Sun·Hua Wang·Xiaohua Yao·Jiqiang Zheng
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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.

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Chenmin Sun, Hua Wang, Xiaohua Yao, Jiqiang Zheng. 2017-02-10. Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data. https://doi.org/10.3934/dcds.2018091

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