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

  • * Corresponding author: Hua Wang

    * Corresponding author: Hua Wang 

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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  • 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.

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


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