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

TL;DR

This paper proves energy decay and scattering for solutions to the defocusing biharmonic Hartree-Fock equations with non-local nonlinearities, extending understanding of long-term behavior in higher dimensions.

Contribution

It establishes energy decay and large-data scattering results for a class of fourth-order Hartree-Fock equations with non-local interactions, including potential perturbations.

Findings

Energy decay in the energy space for solutions.

Large-data scattering in H^2 space.

Results valid for both free and potential-perturbed cases.

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 $d\geq3$. We treat both the free and the perturbed by a potential case. As a direct consequence, we obtain large-data scattering in $H^2(\mathbb R^d)^N, \, N\geq 1$.