Regularized vortex approximation for 2D Euler equations with transport noise

Abstract

We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot-Savart kernel and the same common noise. The approximation happens by sending the number of particles N to infinity and the regularization ǫ in the Biot-Savart kernel to 0, as a suitable function of N .