Scattering theory for a class of radial focusing inhomogeneous Hartree equations

Abstract

This paper studies the asymptotic behavior of global solutions to the generalized Hartree equation $$i\dot{u}+\Delta u+(I_{\alpha }\ast |\cdot {|}^b|u{|}^p)|x{|}^b|u{|}^{p-2}u=0.$$ Indeed, using a new approach due to \cite{dm}, one proves the scattering of the above inhomogeneous Choquard equation in the mass-super-critical and energy sub-critical regimes with radial setting.