Local well-posedness for the (n+1)-dimensional Yang-Mills and Yang-Mills-Higgs system in temporal gauge

TL;DR

This paper proves local well-posedness for the Yang-Mills and Yang-Mills-Higgs systems in temporal gauge across various dimensions, utilizing null structures to handle small, rough initial data.

Contribution

It extends Tao's results on Yang-Mills equations to more general Yang-Mills-Higgs systems and higher dimensions, demonstrating local well-posedness with minimal regularity.

Findings

Established local well-posedness for small, rough initial data

Extended Tao's results to Yang-Mills-Higgs systems in general dimensions

Utilized null structures to control bilinear terms

Abstract

The Yang-Mills and Yang-Mills-Higgs equations in temporal gauge are locally well-posed for small and rough initial data, which can be shown using the null structure of the critical bilinear terms. This carries over a similar result by Tao for the Yang-Mills equations in the (3+1)-dimensional case to the more general Yang-Mills-Higgs system and to general dimensions.