Quantitative Propagation of Chaos for the Mixed-Sign Viscous Vortex Model on the Torus

Abstract

We derive a quantiative propagation of chaos result for a mixed-sign point vortex system on ${\mathbb{T}}^2$ with independent Brownian noise, at an optimal rate. We introduce a pairing between vortices of opposite sign, and using the vorticity formulation of 2D Navier-Stokes, we define an associated tensorized vorticity equation on ${\mathbb{T}}^2\times {\mathbb{T}}^2$ with the same well-posedness theory as the original equation. Solutions of the new PDE can be projected onto solutions of Navier-Stokes, and the tensorized equation allows us to exploit existing propagation of chaos theory for identical particles.

arXiv comment16 pages