Scattering for radial bi-harmonic Hartree equations

Abstract

This note studies the asymptotic behavior of global solutions to the fourth-order generalized Hartree equation $$i\dot{u}+{\Delta }^{2}u\pm (I_{\alpha }\ast |u{|}^p)|u{|}^{p-2}u=0.$$ Indeed, for both attractive and repulsive sign, the scattering is obtained in the mass super-critical and energy sub-critical regimes, with radial setting.