Local well-posedness for the space-time Monopole equation in Lorenz gauge

Abstract

It is known from the work of Czubak that the space-time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in $H^s(\mathbb{R}^2)$ for $s>1/4$. Here we prove local well-posedness for arbitrary initial data in $H^s(\mathbb{R^2})$ with $s>1/4$ in the Lorenz gauge.