Low regularity local well-posedness for the Yang-Mills equation in Lorenz gauge

Abstract

We prove that the Yang-Mills equation in Lorenz gauge in the (n+1)-dimensional case is locally well-posed for data of the gauge potential in $H^s$ and the curvature in $H^r$ , where $s>\frac{n}{2}-\frac{7}{8}$ , $r>\frac{n}{2}-\frac{7}{4}$ , if $n\ge 4$, and $s>\frac{3}{4}$ , $r>-\frac{1}{8}$ , if $n=3$. The proof is based on the fundamental results of Klainerman-Selberg [KS] and on the null structure of most of the nonlinear terms detected by Selberg-Tesfahun [ST] and Tesfahun [Te].

44 pages. In the (3+1)-dimensional case the proof is significantly simplified

References in corpus (1)

• Finite energy global well-posedness of the Yang-Mills equations on ${\mathbb{R}}^{1+3}$: An approach using the Yang-Mills heat flow

Cited by in corpus (1)

• Local well-posedness for the (n+1)-dimensional Maxwell-Klein-Gordon equations in temporal gauge