Desingularized propagating vortex equilibria

The correction to the propagation velocity of point vortex equilibria is calculated by allowing the vortices to have finite core size. A matched asymptotic expansion in the small parameter $\epsilon$, given by the ratio of the core size to the dimension of the configuration, is carried out. The resulting velocity correction is found to be of order $\epsilon^4$ and comes from the interaction of terms in the inner expansion. The results are compared to the known cases of propagating hollow vortex and vortex patch dipoles.