{
  "id": "0811.4647",
  "version": "v2",
  "published": "2008-11-28T05:07:47.000Z",
  "updated": "2009-01-02T22:34:39.000Z",
  "title": "Liouville type of theorems with weights for the Navier-Stokes equations and the Euler equations",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study Liouville type of theorems for the Navier-Stokes and the Euler equations on $\\Bbb R^N$, $N\\geq 2$. Specifically, we prove that if a weak solution $(v,p)$ satisfies $|v|^2 +|p| \\in L^1 (0,T; L^1(\\Bbb R^N, w_1(x)dx))$ and $\\int_{\\Bbb R^N} p(x,t)w_2 (x)dx \\geq0$ for some weight functions $w_1(x)$ and $w_2 (x)$, then the solution is trivial, namely $v=0$ almost everywhere on $\\Bbb R^N \\times (0, T)$. Similar results hold for the MHD Equations on $\\Bbb R^N$, $N\\geq3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-02T22:34:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "euler equations",
      "navier-stokes equations",
      "similar results hold",
      "study liouville type",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.4647C"
    }
  }
}