On global existence for mass-supercritical nonlinear fractional Hartree equations

Abstract

In this paper, we consider the nonlinear fractional Schrodinger equations with Hartree type nonlinearity in mass-supercritical and energy-subcritical case. By sharp Hardy-Littlewood-Sobolev inequality and the Pohozaev identity, we established a threshold condition, which leads to a global existence of solutions in energy space.