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

TL;DR

This paper establishes local well-posedness for the space-time Monopole equation in the Lorenz gauge for initial data with regularity above 1/4, extending previous results from the Coulomb gauge.

Contribution

It proves local well-posedness in the Lorenz gauge for arbitrary initial data in $H^s( ^2)$ with $s>1/4$, broadening the understanding of the equation's behavior.

Findings

Well-posedness holds for all initial data in $H^s( ^2)$ with $s>1/4$ in Lorenz gauge.

Extends previous results from Coulomb gauge to Lorenz gauge.

Provides a new framework for analyzing the space-time Monopole equation.

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.