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

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 $3\mathrm{/}4$ above the critical regularity with respect to scaling. For data in $L^r$-based Fourier-Lebesgue spaces this result can be improved by $1\mathrm{/}4$ derivative in the sense of scaling as $r\to 1$ .