Point vortex approximation for 2D Navier--Stokes equations driven by space-time white noise

TL;DR

This paper demonstrates that a system of point vortices with transport noise converges to the 2D Navier--Stokes equations driven by space-time white noise, providing a stochastic approximation framework.

Contribution

It introduces a novel weak convergence result linking point vortex dynamics with stochastic 2D Navier--Stokes equations driven by white noise.

Findings

Point vortex system converges to stochastic Navier--Stokes equations

Weak convergence established under transport noise perturbation

Provides a stochastic approximation method for fluid dynamics models

Abstract

We show that the system of point vortices, perturbed by a certain transport type noise, converges weakly to the vorticity form of 2D Navier--Stokes equations driven by the space-time white noise.