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


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.


Joachim Krieger

École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

Daniel Tataru

The University of California at Berkeley, Berkeley, CA