{
  "id": "1706.05046",
  "version": "v1",
  "published": "2017-06-15T19:05:03.000Z",
  "updated": "2017-06-15T19:05:03.000Z",
  "title": "On The Two and Three Dimensional Ideal Magnetic Bénard Problem - Local Existence and Blow-up Criterion",
  "authors": [
    "Utpal Manna",
    "Akash A. Panda"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the ideal magnetic B\\'{e}nard problem in both two and three dimensions and prove local-in-time existence and uniqueness of strong solutions in $H^s$ for $s > \\frac{n}{2}+1, n = 2,3$. In addition, a necessary condition is derived for singularity development with respect to the $BMO$-norm of the vorticity and electrical current, generalising the Beale-Kato-Majda condition for ideal hydrodynamics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-15T19:05:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D05",
      "76D03"
    ],
    "keywords": [
      "dimensional ideal magnetic bénard problem",
      "local existence",
      "blow-up criterion",
      "local-in-time existence",
      "strong solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}