Low regularity well-posedness for the Yang-Mills system in 2D

TL;DR

This paper investigates the well-posedness of the 2D Yang-Mills equations with minimal regularity data, improving existing results by lowering the regularity threshold using Fourier-Lebesgue spaces.

Contribution

It extends the well-posedness results for the 2D Yang-Mills system to lower regularity data in Fourier-Lebesgue spaces, surpassing previous Sobolev space limitations.

Findings

Achieved well-posedness for data with less than 3/4 derivatives above critical regularity.

Improved regularity results by 1/4 derivative as Fourier-Lebesgue space parameter r approaches 1.

Demonstrated the effectiveness of Fourier-Lebesgue spaces in low regularity analysis.

Abstract

The Cauchy problem for the Yang-Mills system in two space dimensions is treated for data with minimal regularity assumptions. In the classical case of data in $L^2$-based Sobolev spaces we have to assume that the number of derivatives is more than $3/4$ above the critical regularity with respect to scaling. For data in $L^r$-based Fourier-Lebesgue spaces this result can be improved by $1/4$ derivative in the sense of scaling as $r \to 1$ .