Scattering Theory for a Class of Radial Focusing Inhomogeneous Hartree Equations

This paper studies the asymptotic behavior of global solutions to the generalized Hartree equation $$ i\dot u+{\Delta} u+(I_{\alpha} *|\cdot|^{b}|u|^{p})|x|^{b}|u|^{p-2}u=0 . $$ Indeed, using a new approach due to (Dodson et al. Proc. Amer. Math. Soc. 145(11), 4859–4867, 2017), one proves the scattering of the above inhomogeneous Choquard equation in the mass-super-critical and energy sub-critical regimes with radial setting.