{
  "id": "0907.0871",
  "version": "v5",
  "published": "2009-07-05T15:45:09.000Z",
  "updated": "2009-09-12T08:35:45.000Z",
  "title": "Blowup of C^2 Solutions for the Euler Equations and Euler-Poisson Equations in R^N",
  "authors": [
    "Manwai Yuen"
  ],
  "comment": "7 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we use integration method to show that there is no existence of global $C^{2}$ solution with compact support, to the pressureless Euler-Poisson equations with attractive forces in $R^{N}$. And the similar result can be shown, provided that the uniformly bounded functional:% \\int_{\\Omega(t)}K\\gamma(\\gamma-1)\\rho^{\\gamma-2}(\\nabla\\rho)^{2}% dx+\\int_{\\Omega(t)}K\\gamma\\rho^{\\gamma-1}\\Delta\\rho dx+\\epsilon\\geq -\\delta\\alpha(N)M, where $M$ is the mass of the solutions and $| \\Omega| $ is the fixed volume of $\\Omega(t)$. On the other hand, our differentiation method provides a simpler proof to show the blowup result in \"D. H. Chae and E. Tadmor, \\textit{On the Finite Time Blow-up of the Euler-Poisson Equations in}$R^{N}$, Commun. Math. Sci. \\textbf{6} (2008), no. 3, 785--789.\". Key Words: Euler Equations, Euler-Poisson Equations, Blowup, Repulsive Forces, Attractive Forces, $C^{2}$ Solutions",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-09-12T08:35:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35Q35",
      "35B30"
    ],
    "keywords": [
      "euler equations",
      "finite time blow-up",
      "attractive forces",
      "differentiation method",
      "pressureless euler-poisson equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0871Y"
    }
  }
}