20,988 research outputs found
Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data
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.Comment: This version is an extension of the last version by the first and
fourth author, where the dimensional case is treate
- …