{
  "id": "2303.12257",
  "version": "v1",
  "published": "2023-03-22T01:54:37.000Z",
  "updated": "2023-03-22T01:54:37.000Z",
  "title": "Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space",
  "authors": [
    "Chanwoo Kim",
    "Trinh T. Nguyen"
  ],
  "comment": "52 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A rigorous derivation of point vortex systems from kinetic equations has been a challenging open problem, due to singular layers in the inviscid limit, giving a large velocity gradient in the Boltzmann equations. In this paper, we derive the Helmholtz-Kirchhoff point-vortex system from the hydrodynamic limits of the Boltzmann equations. We construct Boltzmann solutions by the Hilbert-type expansion associated to the point vortices solutions of the 2D Navier-Stokes equations. We give a precise pointwise estimate for the solution of the Boltzmann equations with small Strouhal number and Knudsen number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-22T01:54:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "phase space",
      "boltzmann equations",
      "asymptotics",
      "point vortices solutions",
      "small strouhal number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}