  Long time existence and uniqueness of solutions to the Yang-Mills heat
equation have been proven over a compact 3-manifold with boundary for initial
data of finite energy. In the present paper we improve on previous estimates by
using a Neumann domination technique that allows us to get much better
pointwise bounds on the magnetic field. As in the earlier work, we focus on
Dirichlet, Neumann and Marini boundary conditions. In addition, we show that
the Wilson Loop functions, gauge invariantly regularized, converge as the
parabolic time goes to infinity.
