{
  "id": "1104.3687",
  "version": "v1",
  "published": "2011-04-19T09:50:44.000Z",
  "updated": "2011-04-19T09:50:44.000Z",
  "title": "Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}",
  "authors": [
    "Manwai Yuen"
  ],
  "comment": "6 pages, Key Words: Euler Equations, Navier-Stokes Equations, Analytical Solutions, Elliptic Symmetry, Makino's Solutions, Self-Similar, Drift Phenomena, Emden Equation, Blowup, Global Solutions",
  "journal": "Communications in Nonlinear Science and Numerical Simulation 17 (2012), 4524-4528",
  "doi": "10.1016/j.cnsns.2012.05.022",
  "categories": [
    "math-ph",
    "math.AP",
    "math.DS",
    "math.MP"
  ],
  "abstract": "Based on Makino's solutions with radially symmetry, we extend the corresponding ones with elliptic symmetry for the compressible Euler and Navier-Stokes equations in R^{N} (N\\geq2). By the separation method, we reduce the Euler and Navier-Stokes equations into 1+N differential functional equations. In detail, the velocity is constructed by the novel Emden dynamical system: {<K1.1/>| <K1.1 ilk=\"MATRIX\" > a_{i}(t)=({\\xi}/(a_{i}(t)({\\Pi}a_{k}(t))^{{\\gamma}-1})), for i=1,2,....,N a_{i}(0)=a_{i0}>0, a_{i}(0)=a_{i1} </K1.1> with arbitrary constants {\\xi}, a_{i0} and a_{i1}. Some blowup phenomena or global existences of the solutions obtained could be shown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-19T09:50:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35Q31",
      "35Q30",
      "37C10",
      "37C75",
      "76N10"
    ],
    "keywords": [
      "navier-stokes equations",
      "elliptic symmetry",
      "compressible euler",
      "self-similar solutions",
      "novel emden dynamical system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Communications in Nonlinear Science and Numerical Simulations",
      "year": 2012,
      "month": "Dec",
      "volume": 17,
      "number": 12,
      "pages": 4524
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012CNSNS..17.4524Y"
    }
  }
}