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We prove decay with respect to some Lebesgue norms for a class of Schrödinger 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 Schrödinger–Choquard equations with mass-energy intercritical nonlinearities in any space dimension and of defocusing Hartree–Fock equations, for any dimension d≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d\ge 3$$\end{document}.
Journal of Evolution Equations – Springer Journals
Published: Oct 3, 2020
Keywords: Nonlinear Schrödinger systems; Choquard equation; Hartree–Fock equations; Scattering theory; Weakly coupled equations; 35J10; 35Q55; 35P25
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