{
  "id": "1302.1301",
  "version": "v1",
  "published": "2013-02-06T09:47:50.000Z",
  "updated": "2013-02-06T09:47:50.000Z",
  "title": "Exact solutions with singularities to ideal hydrodynamics of inelastic gases",
  "authors": [
    "Olga S Rozanova"
  ],
  "comment": "8 pages, 4 figures",
  "categories": [
    "math-ph",
    "math.AP",
    "math.MP"
  ],
  "abstract": "We construct a large family of exact solutions to the hyperbolic system of 3 equations of ideal granular hydrodynamics in several dimensions for arbitrary adiabatic index $\\gamma$. In dependence of initial conditions these solutions can keep smoothness for all times or develop singularity. In particular, in the 2D case the singularity can be formed either in a point or along a line. For $\\gamma=-1$ the problem is reduced to the system of two equations, related to a special case of the Chaplygin gas. In the 1D case this system can be written in the Riemann invariant and can be treated in a standard way. The solution to the Riemann problem in this case demonstrate an unusual and complicated behavior.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-06T09:47:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L60",
      "76N10",
      "35L67"
    ],
    "keywords": [
      "exact solutions",
      "inelastic gases",
      "ideal hydrodynamics",
      "singularity",
      "arbitrary adiabatic index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.1301R"
    }
  }
}