Vortex dynamics for 2D Euler flows with unbounded vorticity

It is well known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained a bounded not necessarily simply connected smooth domain described by Kirchhoff–Routh point vortex system. In this paper, we revisit classical problem how solutions to Euler equations approximate these dynamics, and extend previous rigorous results case where vorticity field unbounded. More precisely, establish estimates for 2-Wasserstein distance between empirical measure associated with dynamics. particular, derive estimate on order weak convergence