Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions

Abstract

We prove the decay in the energy space for the solution to the defocusing biharmonic Hartree-Fock equations with mass-supercritical and energy-subcritical Choquard-type nonlinearity in space dimension $d\ge 3$. We treat both the free and the perturbed by a potential case. As a direct consequence, we obtain large-data scattering in $H^2({\mathbb{R}}^d{)}^N,N\ge 1$.