Scattering for radial bi-harmonic Hartree equations

Abstract

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