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

### Abstract

We consider the hyperbolic Yang-Mills equation on the Minkowski space $\mathbb{R}^{4+1}$. 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.

## Authors

Joachim Krieger

École Polytechnique Fédérale de Lausanne (EPFL), Station 8, CH-1015 Lausanne, Switzerland

Daniel Tataru

The University of California at Berkeley, Evans Hall, Berkeley, CA 94720, U.S.A.