{
  "id": "1309.0477",
  "version": "v2",
  "published": "2013-09-02T17:52:50.000Z",
  "updated": "2016-06-14T16:19:11.000Z",
  "title": "Motion of slightly compressible fluids in a bounded domain. II",
  "authors": [
    "Marcelo M. Disconzi",
    "David G. Ebin"
  ],
  "comment": "to appear in Communications in Contemporary Mathematics",
  "categories": [
    "math.AP",
    "math.DG",
    "math.FA",
    "physics.flu-dyn"
  ],
  "abstract": "We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of non-linear equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-02T17:52:50.000Z",
      "abstract": "We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is close to the analogous solution for an incompressible fluid. Furthermore we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for non-linear equations. The results were announced by the first author in Comm. Pure Appl. Math. Vol. XXXV, pp. 451-485.",
      "comment": null,
      "journal": null,
      "doi": null,
      "authors": [
        "David G. Ebin",
        "Marcelo M. Disconzi"
      ]
    },
    {
      "version": "v2",
      "updated": "2016-06-14T16:19:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bounded domain",
      "initial-boundary value problem",
      "unique solution",
      "pure appl",
      "motion problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0477E"
    }
  }
}