  The existence and uniqueness of solutions to the Yang-Mills heat equation
over domains in Euclidean three space was proven in a previous paper for
initial data lying in the Sobolev space of order one-half, which is the
critical Sobolev index for this equation. In the present paper the stability of
these solutions will be established. The variational equation, which is only
weakly parabolic, and has highly singular coefficients, will be shown to have
unique strong solutions up to addition of a vertical solution. Initial data
will be taken to be in Sobolev class one-half. The proof relies on an
infinitesimal version of the ZDS procedure: one solves first an augmented,
strictly parabolic version of the variational equation and then adds to the
solution a function which is vertical along the original path. Energy
inequalities and Neumann domination techniques will be used to establish
apriori initial behavior for solutions.
