• 2d Navier-Stokes equation
• analytic semigroup
• moderately interacting particle system
• stochastic differential equations
• turbulent viscosity
• vorticity equation

The goal of this Thesis is to generalize arguments of the article "Uniform Approximation of 2D Navier-Stokes equation by stochastic interacting particle systems" by Franco Flandoli, Christian Olivera and Marielle Simon to the case of a non-constant viscosity.
Extending the result of their paper, we prove that the mollified empirical measure associated to a stochastic interacting particle system, converges to the unique solution of the PDE in vorticity form. Said particle system consists of a stochastic version of the point vortex dynamics, in which the non-constant viscosity intervenes through the covariance structure of the driving noise. The main difference with the work by F. Flandoli, C. Olivera and M. Simon is encoded in the operator semigroup associated to the linear part of the evolution, as that generated by the elliptic operator in the new PDE in vorticity form does not commute with partial derivatives, as opposed to the heat semigroup. In particular, this prevents us from straightforwardly replicate the estimates in the quoted work, and a different strategy is needed in order to overcome the problem.