{
  "id": "1812.04495",
  "version": "v1",
  "published": "2018-12-10T10:50:53.000Z",
  "updated": "2018-12-10T10:50:53.000Z",
  "title": "On Liouville type theorem for the stationary magnetohydrodynamics system",
  "authors": [
    "Dongho Chae",
    "Joerg Wolf"
  ],
  "comment": "12 pages. arXiv admin note: text overlap with arXiv:1811.09051",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove a Liouville type theorem for the stationary magnetohydrodynamics(MHD) system in $\\Bbb R^3$. Let $(v, B, p)$ be a smooth solution to the stationary MHD equations in $\\Bbb R^3$. We show that if there exist smooth matrix valued potential functions ${\\bf \\Phi}$, ${\\bf \\Psi}$ such that $ \\nabla \\cdot {\\bf \\Phi} =v$ and $\\nabla \\cdot {\\bf \\Psi}= B$, whose $L^6$ mean oscillations have certain growth condition near infinity, namely $$-\\!\\!\\!\\!\\!\\int_{B(r)} |\\mathbf{\\Phi} - \\mathbf{\\Phi}_{ B(r)} |^6 dx + -\\!\\!\\!\\!\\!\\int_{B(r)} |\\mathbf{\\Psi}- \\mathbf{\\Psi}_{ B(r)} |^6 dx\\le C r\\quad \\forall 1< r< +\\infty,$$ then $v=B= 0$ and $p=$constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-10T10:50:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "76D03"
    ],
    "keywords": [
      "liouville type theorem",
      "stationary magnetohydrodynamics system",
      "smooth matrix valued potential functions",
      "stationary mhd equations",
      "smooth solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}