Uniform approximation of 2 dimensional Navier-Stokes equation by stochastic interacting particle systems

We consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-Stokes equation written in vorticity form. The proofs follow a semigroup approach.