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

TL;DR

This paper introduces a particle system model that approximates the 2D Navier-Stokes equation with transport noise, demonstrating uniform convergence of empirical distributions to the PDE solution.

Contribution

It provides a novel stochastic particle approximation method for the 2D Navier-Stokes equation with transport noise, using a semigroup approach.

Findings

Empirical distribution converges uniformly to the PDE solution.

The model effectively captures the dynamics of the Navier-Stokes equation with noise.

The approach offers a new tool for analyzing stochastic fluid dynamics.

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.