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 $B_{2,1}^{\frac{1}{2}}\times B_{2,1}^{-\frac{1}{2}}$ 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.

Lemma 2.3 is incorrect. More delicate decomposition is needed