{
  "id": "1709.01319",
  "version": "v1",
  "published": "2017-09-05T10:17:19.000Z",
  "updated": "2017-09-05T10:17:19.000Z",
  "title": "Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations",
  "authors": [
    "Yanqing Wang",
    "Gang Wu"
  ],
  "comment": "submitted on 19 Mar. 2017",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, let $\\mathcal{S}$ denote the possible interior singular set of suitable weak solutions of the 3D Navier-Stokes equations. We improve the known upper box-counting dimension of this set from $360/277(\\approx1.300)$ in [24] to $975/758(\\approx1.286)$. It is also shown that $\\Lambda(\\mathcal{S},r(\\log(e/r))^{\\sigma})=0(0\\leq\\sigma<7/23)$, which extends the previous corresponding results concerning the improvement of the classical Caffarelli-Kohn-Nirenberg theorem by a logarithmic factor. The proof rests on a new $\\varepsilon$-regularity criterion proved by Guevara and Phuc in [7, Calc. Var. 56:68, 2017] and establishing associated decay-type estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-05T10:17:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d navier-stokes equations",
      "suitable weak solutions",
      "interior singular set",
      "logarithmic factor",
      "classical caffarelli-kohn-nirenberg theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}