{
  "id": "1209.6522",
  "version": "v2",
  "published": "2012-09-28T13:58:55.000Z",
  "updated": "2013-05-28T16:25:52.000Z",
  "title": "Solenoidal Lipschitz truncation for parabolic PDE's",
  "authors": [
    "D. Breit",
    "L. Diening",
    "S. Schwarzacher"
  ],
  "journal": "Annali.di.Matematica.Pura.ed.Applicata 23 (2013) 2671-2700",
  "doi": "10.1142/S0218202513500437",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider functions $u\\in L^\\infty(L^2)\\cap L^p(W^{1,p})$ with $1<p<\\infty$ on a time space domain. Solutions to non-linear evolutionary PDE's typically belong to these spaces. Many applications require a Lipschitz approximation $u_\\lambda$ of $u$ which coincides with $u$ on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids in [DRW10]. Since ${\\rm div} u_\\lambda=0$, we are able to work in the pressure free formulation, which heavily simplifies the proof. We also provide a simplified approach to the stationary solenoidal Lipschitz truncation of [BDF12].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-28T16:25:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B03",
      "35D05",
      "35J60",
      "26B35"
    ],
    "keywords": [
      "parabolic pdes",
      "stationary solenoidal lipschitz truncation",
      "non-linear evolutionary pdes typically belong",
      "lipschitz approximation",
      "time space domain"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.6522B"
    }
  }
}