Long Range Scattering for the Maxwell–Schrödinger System with Large Magnetic Field Data and Small Schrödinger Data

Abstract

We study the theory of scattering for the Maxwell–Schrödinger system in the Coulomb gauge in space dimension 3. We prove in particular the existence of modified wave operators for that system with no size restriction on the magnetic field data in the framework of a direct method which requires smallness of the Schrödinger data, and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.