{
  "id": "1505.00142",
  "version": "v1",
  "published": "2015-05-01T10:06:39.000Z",
  "updated": "2015-05-01T10:06:39.000Z",
  "title": "Structure of Helicity and Global Solutions of Incompressible Navier-Stokes Equation",
  "authors": [
    "Zhen Lei",
    "Fang-Hua Lin",
    "Yi Zhou"
  ],
  "comment": "To appear in ARMA",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we derive a new energy identity for the three-dimensional incompressible Navier-Stokes equations by a special structure of helicity. The new energy functional is critical with respect to the natural scalings of the Navier-Stokes equations. Moreover, it is conditionally coercive. As an application we construct a family of finite energy smooth solutions to the Navier-Stokes equations whose critical norms can be arbitrarily large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-01T10:06:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global solutions",
      "finite energy smooth solutions",
      "three-dimensional incompressible navier-stokes equations",
      "energy functional",
      "energy identity"
    ],
    "publication": {
      "doi": "10.1007/s00205-015-0884-8",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2015,
      "month": "Dec",
      "volume": 218,
      "number": 3,
      "pages": 1417
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015ArRMA.218.1417L"
    }
  }
}