On the scaling critical regularity of the Yang-Mills system in the Lorenz gauge

Abstract

In this paper, we prove the local well-posedness of the Yang-Mills system in the Lorenz gauge for initial data in the Besov space $B^\frac12_{2,1}\times B^{-\frac12}_{2,1}$ with additional angular regularity. To the best of our knowledge, our study is the first result on $(1+3)$ dimensional Yang-Mills system with initial data in the scaling critical regularity.