{
  "id": "1909.08678",
  "version": "v1",
  "published": "2019-09-18T20:06:59.000Z",
  "updated": "2019-09-18T20:06:59.000Z",
  "title": "Bounded solutions of ideal MHD with compact support in space-time",
  "authors": [
    "Daniel Faraco",
    "Sauli Lindberg",
    "László Székelyhidi Jr"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and magnetic fields. The solutions violate conservation of total energy and cross helicity, but preserve magnetic helicity. For the 2-dimensional case we show that, in contrast, no nontrivial compactly supported solutions exist in the energy space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-18T20:06:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "76W05",
      "76B03"
    ],
    "keywords": [
      "bounded solutions",
      "compact support",
      "ideal mhd",
      "space-time",
      "preserve magnetic helicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}