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