{
  "id": "2106.05255",
  "version": "v1",
  "published": "2021-06-09T17:54:25.000Z",
  "updated": "2021-06-09T17:54:25.000Z",
  "title": "Quantitative Propagation of Chaos for the Mixed-Sign Viscous Vortex Model on the Torus",
  "authors": [
    "Dominic Wynter"
  ],
  "comment": "16 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-09T17:54:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mixed-sign viscous vortex model",
      "quantitative propagation",
      "mixed-sign point vortex system",
      "independent brownian noise",
      "chaos result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}