{
  "id": "1509.01952",
  "version": "v1",
  "published": "2015-09-07T09:03:23.000Z",
  "updated": "2015-09-07T09:03:23.000Z",
  "title": "On the critical one component regularity for 3-D Navier-Stokes system: general case",
  "authors": [
    "Jean-Yves Chemin",
    "Ping Zhang",
    "Zhifei Zhang"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1310.6442",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let us consider an initial data $v_0$ for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to $L^{\\frac 32}\\cap L^2$. We prove that if the solution associated with $v_0$ blows up at a finite time $T^\\star$, then for any $p$ in $]4,\\infty[$, and any unit vector $e$ of $\\R^3$, the $L^p$ norm in time with value in $\\dot{H}^{\\frac 12+\\frac 2 p }$ of $(v|e)_{\\R^3}$ blows up at $T^\\star$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-07T09:03:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03"
    ],
    "keywords": [
      "navier-stokes system",
      "component regularity",
      "general case",
      "homogeneous incompressible 3d navier-stokes equation",
      "unit vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901952C"
    }
  }
}