Low regularity well-posedness for the Yang-Mills system in Fourier-Lebesgue spaces

TL;DR

This paper proves local well-posedness for the Yang-Mills system in three dimensions with initial data in Fourier-Lebesgue spaces, achieving minimal regularity assumptions even without known null conditions.

Contribution

It extends well-posedness results to Fourier-Lebesgue spaces with minimal regularity, overcoming limitations of classical Sobolev space approaches.

Findings

Local well-posedness established for Fourier-Lebesgue spaces $\hat{H}^{s,r}$ with $1<r extless=2$

Results hold despite absence of null condition for critical quadratic nonlinearities

Achieves near-optimal regularity with respect to scaling as $r o 1$

Abstract

The Cauchy problem for the Yang-Mills system in three space dimensions with data in Fourier-Lebesgue spaces $\hat{H}^{s,r}$ , $1 < r \le 2$ , is shown to be locally well-posed, where we have to assume only almost optimal minimal regularity for the data with respect to scaling as $r \to 1$ . This is true despite of the fact that no null condition is known for one of the critical quadratic nonlinearities, which prevented by now the corresponding result in the classical case $r=2$ with data in standard Sobolev spaces.