The Yang-Mills heat flow with random distributional initial data

We construct local solutions to the Yang–Mills heat flow (in DeTurck gauge) for a certain class of random distributional initial data, which includes 3D Gaussian free field. The main idea, goes back work Bourgain as well Da Prato–Debussche, is decompose solution into rougher linear part and smoother nonlinear part, control latter by probabilistic arguments. In companion work, we use results this paper propose way toward construction measures.