Long range scattering for the Maxwell-Schr"odinger system with arbitrarily large asymptotic data

TL;DR

This paper reviews the proof of existence and uniqueness of solutions to the Maxwell-Schrödinger system near infinity in time, accommodating arbitrarily large asymptotic data, which is crucial for constructing modified wave operators.

Contribution

It establishes existence and uniqueness results for the Maxwell-Schrödinger system with large asymptotic data without size restrictions, advancing the understanding of long-range scattering.

Findings

Proves existence and uniqueness of solutions near infinity

Handles arbitrarily large asymptotic data

Supports construction of modified wave operators

Abstract

We review the proof of existence and uniqueness of solutions of the Maxwell-Schr"odinger system in a neighborhood of infinity in time, with prescribed asymptotic behaviour defined in terms of asymptotic data, without any restriction on the size of those data. That result is the basic step in the construction of modified wave operators for the Maxwell-Schr"odinger system.