{
  "id": "2110.04674",
  "version": "v2",
  "published": "2021-10-10T01:11:11.000Z",
  "updated": "2022-03-22T20:19:34.000Z",
  "title": "On the vanishing viscosity limit of statistical solutions of the incompressible Navier-Stokes equations",
  "authors": [
    "Ulrik Skre Fjordholm",
    "Siddhartha Mishra",
    "Franziska Weber"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study statistical solutions of the incompressible Navier-Stokes equation and their vanishing viscosity limit. We show that a formulation using correlation measures, which are probability measures accounting for spatial correlations, and moment equations is equivalent to statistical solutions in the Foias-Prodi sense. Under the assumption of weak scaling, a weaker version of Kolmogorov's self-similarity at small scales hypothesis that allows for intermittency corrections, we show that the limit is a statistical solution of the incompressible Euler equations. To pass to the limit, we derive a Karman-Howarth-Monin relation for statistical solutions and combine it with the weak scaling assumption and a compactness theorem for correlation measures.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-22T20:19:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "statistical solution",
      "incompressible navier-stokes equation",
      "vanishing viscosity limit",
      "correlation measures",
      "small scales hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}