Local well-posedness of the Yang–Mills equation in the temporal gauge below the energy norm

We show that the Yang–Mills equation in three dimensions in the temporal gauge is locally well-posed in Hs for if the Hs norm is sufficiently small. The temporal gauge is slightly less convenient technically than the more popular Coulomb gauge, but has the advantage of uniqueness even for large initial data, and does not require solving a nonlinear elliptic problem. To handle the temporal gauge correctly we project the connection into curl- and divergence-free components, and develop some new bilinear estimates of Xs,b type which can handle integration in the time direction.