Decay of solutions of Maxwell-Klein-Gordon equations with large Maxwell field

TL;DR

This paper establishes pointwise decay estimates for solutions to the Maxwell-Klein-Gordon equations in 3+1 dimensions, allowing large initial Maxwell fields but small scalar fields, extending previous decay results.

Contribution

It proves decay estimates under weaker initial data assumptions, specifically large Maxwell fields with small scalar fields, broadening the understanding of solution behavior.

Findings

Solutions exhibit pointwise decay despite large Maxwell initial data.

Extends decay results to cases with large Maxwell fields and small scalar fields.

Builds on and generalizes previous decay theorems.

Abstract

It has been shown in the author's companion paper that solutions of Maxwell-Klein-Gordon equations in $\mathbb{R}^{3+1}$ possess some form of global strong decay properties with data bounded in some weighted energy space. In this paper, we prove pointwise decay estimates for the solutions for the case when the initial data are merely small on the scalar field but can be arbitrarily large on the Maxwell field. This extends the previous result of Lindblad-Sterbenz \cite{LindbladMKG}, in which smallness was assumed both for the scalar field and the Maxwell field.