{
  "id": "math/0503425",
  "version": "v1",
  "published": "2005-03-21T15:19:07.000Z",
  "updated": "2005-03-21T15:19:07.000Z",
  "title": "Well-posedness of a multiscale model for concentrated suspensions",
  "authors": [
    "Eric Cancès",
    "Isabelle Catto",
    "Yousra Gati",
    "Claude Le Bris"
  ],
  "comment": "1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In a previous work [math.AP/0305408] three of us have studied a nonlinear parabolic equation arising in the mesoscopic modelling of concentrated suspensions of particles that are subjected to a given time-dependent shear rate. In the present work we extend the model to allow for a more physically relevant situation when the shear rate actually depends on the macroscopic velocity of the fluid, and as a feedback the macroscopic velocity is influenced by the average stress in the fluid. The geometry considered is that of a planar Couette flow. The mathematical system under study couples the one-dimensional heat equation and a nonlinear Fokker-Planck type equation with nonhomogeneous, nonlocal and possibly degenerate, coefficients. We show the existence and the uniqueness of the global-in-time weak solution to such a system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-21T15:19:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K65",
      "35Q35",
      "76A05",
      "76A10"
    ],
    "keywords": [
      "concentrated suspensions",
      "multiscale model",
      "well-posedness",
      "nonlinear fokker-planck type equation",
      "macroscopic velocity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3425C"
    }
  }
}