A uniform point vortex approximation for the solution of the two-dimensional Navier Stokes equation with transport noise

Abstract

We study a model of interacting particles represented by a system of N stochastic differential equations. We establish that the mollified empirical distribution of the system converges uniformly with respect to both time and spatial variables to the solution of the two dimensional Navier Stokes equation with transport noise. The proofs are based on a semigroup approach.