{
  "id": "1203.6799",
  "version": "v1",
  "published": "2012-03-30T13:01:15.000Z",
  "updated": "2012-03-30T13:01:15.000Z",
  "title": "A note about existence for a class of viscous fluid problems",
  "authors": [
    "Hermenegildo Borges de Oliveira"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent $q$ that characterizes the flow depends on the space variable: $q=q(\\mathbf{x})$. For the associated boundary-value problem we show that, in some situations, the log-H\\\"older continuity condition on $q$ can be dropped and the result of the existence of weak solutions still remain valid for any variable exponent $q\\geq\\alpha>\\frac{2N}{N+2}$, where $\\alpha=\\mathrm{ess}\\inf q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-30T13:01:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "76D05",
      "35J60",
      "35Q30",
      "35Q35"
    ],
    "keywords": [
      "weak solutions",
      "non-newtonian viscous fluid problems",
      "steady case",
      "generalized navier-stokes equations",
      "flow depends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.6799B"
    }
  }
}