Global well-posedness for the Maxwell-Klein Gordon equation in 4+1 dimensions. Small energy

TL;DR

This paper proves global well-posedness for the critical Maxwell-Klein Gordon equation in 4+1 dimensions for small energy initial data, reducing the large data problem to energy concentration prevention.

Contribution

It establishes global regularity for small energy initial data, advancing understanding of the Maxwell-Klein Gordon equation in higher dimensions.

Findings

Global well-posedness for small energy data

Reduction of large data problem to energy concentration issues

Framework for analyzing critical nonlinear wave equations

Abstract

We prove that the critical Maxwell-Klein Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy. This reduces the problem of global regularity for large, smooth initial data to precluding concentration of energy.