Local well-posedness of Yang-Mills equations in Lorenz gauge below the energy norm

We prove that the Yang-Mills equations in the Lorenz gauge (YM-LG) is locally well-posed for data below the energy norm, in particular, we can take data for the gauge potential A and the associated curvature , respectively. This extends a recent result by Selberg and the present author on the local well-posedness of YM-LG for finite energy data (specifically, for (s, r) = (1-, 0)). We also prove unconditional uniqueness of the energy class solution, that is, uniqueness in the classical space C([-T, T]; X (0)), where X (0) is the energy data space. The key ingredient in the proof is the fact that most bilinear terms in YM-LG contain null structure some of which uncovered in the present paper.