{
  "id": "0911.2756",
  "version": "v1",
  "published": "2009-11-14T09:12:32.000Z",
  "updated": "2009-11-14T09:12:32.000Z",
  "title": "Well-posedness of the equations of a viscoelastic fluid with a free boundary",
  "authors": [
    "Hervé Le Meur"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we prove the local well-posedness, for arbitrary initial data with certain regularity assumptions, of the equations of a Viscoelastic Fluid of Johnson-Segalman type with a free surface. More general constitutive laws can be easily managed in the same way. The geometry is defined by a solid fixed bottom and an upper free boundary submitted to surface tension. The proof relies on a Lagrangian formulation. First we solve two intermediate problems through a fixed point using mainly G. Allain Appl. Math. Optim. 16 (1987) 37-50 for the Navier-Stokes part. Then we solve the whole Lagrangian problem on $[0,T_0]$ for $T_0$ small enough through a contraction mapping. Since the Lagrangian solution is smooth, we can come back to an Eulerian one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-14T09:12:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35Q35",
      "76D03",
      "76D05",
      "76N10"
    ],
    "keywords": [
      "viscoelastic fluid",
      "well-posedness",
      "arbitrary initial data",
      "upper free boundary",
      "lagrangian problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.2756L"
    }
  }
}