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

2019/04/23 by Tarulli, Mirko, Venkov, George
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1904.10364

Abstract

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.

Related

• Decay in energy space for the solution of fourth-order Hartree-Fock equations with general non-local interactions
• Decay of solutions to one-dimensional inhomogeneous nonlinear Schrödinger equations
• Scattering for the non-radial focusing inhomogeneous nonlinear Schrödinger-Choquard equation
• Modified Scattering for Nonlocal Nonlinear Schrödinger Equations
• H²-scattering for systems of weakly coupled fourth-order NLS equations in low space dimensions