Quantitative particle approximations of stochastic 2D Navier-Stokes equation

In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the stochastic 2-dimensional Navier-Stokes equation. We establish a quantitative mean-field convergence for the stochastic 2-dimensional Navier-Stokes equation in the form of relative entropy. To address challenges posed by environmental noise, random intensities, and singular kernel, we compare relative entropy for conditional distributions, employing technology of disintegration and the relative entropy method developed by Jabin and Wang in [JW18].