{
  "id": "1903.05483",
  "version": "v1",
  "published": "2019-03-13T13:46:51.000Z",
  "updated": "2019-03-13T13:46:51.000Z",
  "title": "On the Vanishing of some D-solutions to the Stationary Magnetohydrodynamics System",
  "authors": [
    "Zijin Li",
    "Xinghong Pan"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the stationary magnetohydrodynamics system in $\\mathbb{R}^2\\times\\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this Liouville type theorem also holds provided $u$ is swirl-free and $h$ is axially symmetric, or both $u$ and $h$ are axially symmetric. Our method is also valid for certain related boundary value problems in the slab $\\mathbb{R}^2\\times[-\\pi,\\,\\pi]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-13T13:46:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76N10"
    ],
    "keywords": [
      "stationary magnetohydrodynamics system",
      "d-solutions",
      "related boundary value problems",
      "liouville type theorem",
      "axially symmetric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}