{
  "id": "1206.5329",
  "version": "v1",
  "published": "2012-06-22T21:59:44.000Z",
  "updated": "2012-06-22T21:59:44.000Z",
  "title": "Nonlinear stabilitty for steady vortex pairs",
  "authors": [
    "Geoffrey R. Burton",
    "Milton C. Lopes Filho",
    "Helena J. Nussenzveig Lopes"
  ],
  "comment": "25 pages",
  "journal": "Comm. Math. Phys. 324 (2013) 445-463",
  "categories": [
    "math.AP",
    "physics.flu-dyn"
  ],
  "abstract": "In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-22T21:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B47",
      "35Q31"
    ],
    "keywords": [
      "steady vortex pairs",
      "nonlinear stabilitty",
      "two-dimensional euler equations",
      "kelvins variational principle",
      "time-dependent euler equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "doi": "10.1007/s00220-013-1806-y",
      "year": 2013,
      "month": "Dec",
      "volume": 324,
      "number": 2,
      "pages": 445
    },
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.324..445B"
    }
  }
}