摘要
In this paper,we study the well-posedness and blow-up solutions for the fractional Schrodinger equation with a Hartree-type nonlinearity together with a power-type subcritical or criticai perturbations.For nonradial initial data or radial initial data,we prove the local well-posedness for the defocusing and the focusing cases with sub-critical or critical nonlinearity.We obtain the global well-posedness for the defocusing case,and for the focusing mass-subcritical case or mass-critical case with initial da-ta small enough.We also investigate blow-up solutions for the focusing mass-critical problem.
基金
This research is supported by NSFC key project under the grant number 11831003
NSFC under the grant numbers 11971356 and 11571118
by Fundamental Research Founds for the Central Universities under the grant numbers 2019MS110 and 2019MS112.
