{
  "id": "1210.0487",
  "version": "v1",
  "published": "2012-10-01T17:58:38.000Z",
  "updated": "2012-10-01T17:58:38.000Z",
  "title": "The lifetime of shape oscillations of a bubble in an unbounded, inviscid and compressible fluid with surface tension",
  "authors": [
    "Ovidiu Costin",
    "Saleh Tanveer",
    "Michael I. Weinstein"
  ],
  "comment": "14 pages, submitted",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "physics.flu-dyn"
  ],
  "abstract": "General perturbations of a spherical gas bubble in a compressible and inviscid fluid with surface tension were proved in Shapiro and Weinstein (2011), in the linearized approximation, to decay exponentially, $\\sim e^{-\\Gamma t}, \\Gamma>0$, as time advances. Formal asymptotic and numerical evidence led to the conjecture that $\\Gamma \\approx \\frac{A}{\\epsilon} \\frac{We}{\\epsilon^{2}} \\exp(-B \\frac{We}{\\epsilon^2})$, where $0<\\epsilon\\ll1$ is the Mach number, We is the Weber number, and $A$ and $B$ are positive constants. In this paper, we prove this conjecture and calculate $A$ and $B$ to leading order in $\\epsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-01T17:58:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surface tension",
      "shape oscillations",
      "compressible fluid",
      "general perturbations",
      "inviscid fluid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0487C"
    }
  }
}