Article ID Journal Published Year Pages File Type
4609229 Journal of Differential Equations 2017 29 Pages PDF
Abstract

In this paper we consider scattering problem for Hartree type fractional NLS with |∇|α|∇|α (1<α<21<α<2) and potential V∼|x|−γV∼|x|−γ. We show small data scattering in a weighted space for the short range 6−2α4−α<γ<2. The difficulty arises from the non-locality and non-smoothness of |∇|α|∇|α. To overcome it we utilize the method of commutator estimate based on Balakrishnan's formula.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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