{
  "id": "0907.2348",
  "version": "v1",
  "published": "2009-07-14T13:22:24.000Z",
  "updated": "2009-07-14T13:22:24.000Z",
  "title": "Axisymmetric Euler-$α$ Equations without Swirl: Existence, Uniqueness, and Radon Measure Valued Solutions",
  "authors": [
    "Quansen Jiu",
    "Dongjuan Niu",
    "Edriss S. Titi",
    "Zhouping Xin"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The global existence of weak solutions for the three-dimensional axisymmetric Euler-$\\alpha$ (also known as Lagrangian-averaged Euler-$\\alpha$) equations, without swirl, is established, whenever the initial unfiltered velocity $v_0$ satisfies $\\frac{\\nabla \\times v_0}{r}$ is a finite Randon measure with compact support. Furthermore, the global existence and uniqueness, is also established in this case provided $\\frac{\\nabla \\times v_0}{r} \\in L^p_c(\\mathbb{R}^3)$ with $p>{3/2}$. It is worth mention that no such results are known to be available, so far, for the three-dimensional Euler equations of ideal incompressible flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-14T13:22:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B47",
      "35Q30"
    ],
    "keywords": [
      "radon measure valued solutions",
      "axisymmetric",
      "uniqueness",
      "global existence",
      "finite randon measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2348J"
    }
  }
}