Scattering for the Non-Radial Defocusing Nonlinear Inhomogeneous Hartree Equation

Abstract

The purpose of this paper is to study scattering theory for the energy subcritical solutions to the non-radial defocusing inhomogeneous Hartree equation

$i \partial_{t} u+\Delta u=\left(I_{\alpha} *|\cdot|^{b}|u|^{p}\right)|\cdot|^{b}|u|^{p-2} u.$

Taking advantage of the decay factor in the nonlinearity instead of the embedding theorem, we establish the scattering criterion for the equation. Together with the Morawetz estimate, we obtain the scattering theory for the energy-subcritical case.

Keywords

Inhomogeneous Hartree equation / scattering theory / Strichartz estimates / Morawetz estimate