{
  "id": "2006.11861",
  "version": "v1",
  "published": "2020-06-21T18:00:07.000Z",
  "updated": "2020-06-21T18:00:07.000Z",
  "title": "Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent",
  "authors": [
    "Kazuo Yamazaki"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Lions (1959, Bull. Soc. Math. France, \\textbf{87}, 245--273) introduced the Navier-Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanov$\\acute{\\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]), we prove the non-uniqueness in law for the three-dimensional stochastic Navier-Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-21T18:00:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A02",
      "35Q30",
      "35R60"
    ],
    "keywords": [
      "non-uniqueness",
      "three-dimensional stochastic navier-stokes equations",
      "fractional laplacian",
      "viscous diffusion",
      "spatial dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}