Global well-posedness for the Yang-Mills equation in $4+1$ dimensions. Small energy

TL;DR

This paper proves that the hyperbolic Yang-Mills equation in 4+1 dimensions is globally well-posed for small initial energy, resolving a longstanding open problem in mathematical physics.

Contribution

It establishes the global well-posedness of the Yang-Mills equation in 4+1 dimensions for small energy initial data, a significant advancement in the field.

Findings

Global well-posedness for small energy initial data

Solution exists for all time in 4+1 dimensions

Addresses a longstanding open problem in Yang-Mills theory

Abstract

We consider the hyperbolic Yang-Mills equation on the Minkowski space $\R^{4+1}$. Our main result asserts that this problem is globally well-posed for all initial data whose energy is sufficiently small. This solves a longstanding open problem.