Scattering theory for a class of radial focusing inhomogeneous Hartree equations

TL;DR

This paper investigates the long-term behavior of solutions to a class of radial inhomogeneous Hartree equations, demonstrating scattering in specific regimes using a novel analytical approach.

Contribution

It introduces a new method to prove scattering for inhomogeneous Hartree equations in mass-super-critical and energy sub-critical regimes with radial symmetry.

Findings

Proves scattering for the inhomogeneous Hartree equation in specified regimes.

Develops a new analytical approach based on prior work by .

Establishes asymptotic behavior of global solutions in the radial setting.

Abstract

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 \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.