{
  "id": "2505.00885",
  "version": "v2",
  "published": "2025-05-01T22:01:19.000Z",
  "updated": "2025-05-15T01:09:41.000Z",
  "title": "Liouville type theorem for double Beltrami solutions of the Hall-MHD system in $\\Bbb R^3$",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "There is a calculation mistake, and the result is not yet valid",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove Liouville type theorem for the double Beltrami solutions to the stationary Hall-MHD equations in $\\Bbb R^3$. Let $(u, B)$ be a smooth double Beltrami solution to the stationary Hall-MHD equations in $\\Bbb R^3$, satisfying $\\int_{\\Bbb R^3} (|u|^q + |B|^q )dx <+\\infty$ for some $q\\in [2, 3)$, then $u=B=0$. In the case of $B=0$ the theorem reduces the previously known Liouville type result for the Beltrami solutions to the Euler equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-05-15T01:09:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "76D03"
    ],
    "keywords": [
      "liouville type theorem",
      "hall-mhd system",
      "stationary hall-mhd equations",
      "smooth double beltrami solution",
      "liouville type result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}