  We study the 2D Navier--Stokes solution starting from an initial vorticity
mildly concentrated near $N$ distinct points in the plane. We prove
quantitative estimates on the propagation of concentration near a system of
interacting point vortices introduced by Helmholtz and Kirchhoff. Our work
extends the previous results in the literature in three ways: The initial
vorticity is concentrated in a weak (Wasserstein) sense, it is merely $L^p$
integrable for some $p>2$, and the estimates we derive are uniform with respect
to the viscosity.
