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arXiv · 2106.05255

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

Dominic Wynter
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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.

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Dominic Wynter. 2021-06-09. Quantitative Propagation of Chaos for the Mixed-Sign Viscous Vortex Model on the Torus. https://arxiv.org/abs/2106.05255

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