Uniform approximation of 2D Navier-Stokes equations with vorticity creation by stochastic interacting particle systems

Abstract

We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2D Navier–Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier–Stokes equations.