{
  "id": "1811.09051",
  "version": "v1",
  "published": "2018-11-22T07:48:36.000Z",
  "updated": "2018-11-22T07:48:36.000Z",
  "title": "On Liouville type theorem for the stationary Navier-Stokes equations",
  "authors": [
    "Dongho Chae",
    "Joerg Wolf"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove a Liouville type theorem in $\\mathbb{R}^3$. Let $(u, p)$ be a smooth solution to the stationary Navier-Stokes equations in $\\mathbb{R}^3$. We show that if there exists matrix valued potential function $\\mathbf{V}$ such that $ \\nabla \\cdot \\mathbf{V} =u$, whose $L^6$ mean oscillation has certain growth condition near infinity, namely $$\\int_{B(r)} |\\mathbf{V}- \\mathbf{V}_{ B(r)} |^6 dx \\le C r\\quad \\forall 1< r< +\\infty,$$ then $u\\equiv 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-22T07:48:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "76D03"
    ],
    "keywords": [
      "stationary navier-stokes equations",
      "liouville type theorem",
      "matrix valued potential function",
      "smooth solution",
      "mean oscillation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}