Decay and scattering in energy space for the solution of weakly coupled Schrödinger–Choquard and Hartree–Fock equations

Abstract

We prove decay with respect to some Lebesgue norms for a class of Schrodinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space for the solutions to the systems of N defocusing Schrodinger–Choquard equations with mass-energy intercritical nonlinearities in any space dimension and of defocusing Hartree–Fock equations, for any dimension $$d\ge 3$$ .