Unconditional global well-posedness in energy space for the Maxwell-Klein-Gordon system in temporal gauge

TL;DR

This paper proves that the Maxwell-Klein-Gordon system in temporal gauge is globally well-posed in energy space with unconditional uniqueness, and also establishes local well-posedness for large data below energy space.

Contribution

It establishes unconditional global well-posedness in energy space and extends local well-posedness results to large data below energy space.

Findings

Unconditional global well-posedness in energy space.

Uniqueness holds in the natural solution space.

Local well-posedness for large data below energy space.

Abstract

The Maxwell-Klein-Gordon system in temporal gauge is unconditionally globally well-posed in energy space, especially uniqueness holds in the natural solution space. This improves earlier results where uniqueness was only shown in a suitable subspace. It is also locally well-posed for large data below energy space.