Quantitative propagation of chaos for the mixed-sign viscous vortex model on the torus

We derive a quantitative propagation of chaos result for a mixed-sign point vortex system on \begin{document}$ \mathbb{T}^2 $\end{document} with independent Brownian noise, at an optimal rate. We introduce a pairing between vortices of opposite sign, and using the vorticity formulation of 2D Navier-Stokes, we define an associated tensorized vorticity equation on \begin{document}$ \mathbb{T}^2\times \mathbb{T}^2 $\end{document} 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.