{
  "id": "1512.00310",
  "version": "v1",
  "published": "2015-12-01T15:52:07.000Z",
  "updated": "2015-12-01T15:52:07.000Z",
  "title": "Anelastic Approximation of the Gross-Pitaevskii equation for General Initial Data",
  "authors": [
    "Chi-Kun Lin",
    "Kung-Chien Wu"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We perform a rigorous analysis of the anelastic approximation for the Gross-Pitaevskii equation with $x$-dependent chemical potential. For general initial data and periodic boundary condition, we show that as $\\eps\\to 0$, equivalently the Planck constant tends to zero, the density $|\\psi^{\\eps}|^{2}$ converges toward the chemical potential $\\rho_{0}(x)$ and the velocity field converges to the anelastic system. When the chemical potential is a constant, the anelastic system will reduce to the incompressible Euler equations. The resonant effects the singular limit process and it can be overcome because of oscillation-cancelation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-01T15:52:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general initial data",
      "anelastic approximation",
      "gross-pitaevskii equation",
      "chemical potential",
      "anelastic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}