{
  "id": "1807.10017",
  "version": "v1",
  "published": "2018-07-26T08:53:48.000Z",
  "updated": "2018-07-26T08:53:48.000Z",
  "title": "Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations",
  "authors": [
    "Claudia García",
    "Taoufik Hmidi",
    "Juan Soler"
  ],
  "comment": "115 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform densities and with different $m$--fold symmetries, $m\\ge 1$. In particular, a complete study is provided for the truncated quadratic density $(A|x|^2+B){\\bf{1}}_{\\mathbb{D}}(x)$, with $\\mathbb{D}$ the unit disc. We exhibit different behaviors with respect to the coefficients $A$ and $B$ describing the rarefaction of bifurcating curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-26T08:53:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35Q35",
      "76B03",
      "76B03",
      "76U05",
      "35B32",
      "35P30"
    ],
    "keywords": [
      "non uniform rotating vortices",
      "two-dimensional euler equations",
      "periodic orbits",
      "construct non trivial",
      "non radial rotating vortices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 115,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}