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

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.