{
  "id": "1102.5436",
  "version": "v1",
  "published": "2011-02-26T19:05:31.000Z",
  "updated": "2011-02-26T19:05:31.000Z",
  "title": "New entropy for Korteweg's system, existence of global weak solution and Prodi-Serrin theorem",
  "authors": [
    "B Haspot"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This work is devoted to prove new entropy estimates for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see \\cite{fDS}), which can be used as a phase transition model. More precisely we will derive new estimates for the density and we will give a new structure for the Korteweg system which allow us to obtain the existence of global weak solution. The key of the proof comes from the introduction of a new effective velocity.The proof is widely inspired from the works of A. Mellet and A. Vasseur (see \\cite{fMV}). In a second part, we shall give a Prody-Serrin blow-up criterion for this system which widely improves the results of \\cite{Hprepa} and the known results on compressible systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-26T19:05:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global weak solution",
      "kortewegs system",
      "prodi-serrin theorem",
      "phase transition model",
      "prody-serrin blow-up criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.5436H"
    }
  }
}