{
  "id": "0912.3958",
  "version": "v2",
  "published": "2009-12-20T02:16:33.000Z",
  "updated": "2010-01-05T00:05:41.000Z",
  "title": "On Optimal Estimates for the Laplace-Leray Commutator in Planar Domains with Corners",
  "authors": [
    "Elaine Cozzi",
    "Robert L. Pego"
  ],
  "comment": "Changed the Latex format",
  "categories": [
    "math.AP"
  ],
  "abstract": "For smooth domains, Liu et al. (Comm. Pure Appl. Math. 60: 1443-1487, 2007) used optimal estimates for the commutator of the Laplacian and the Leray projection operator to establish well-posedness of an extended Navier-Stokes dynamics. In their work, the pressure is not determined by incompressibility, but rather by a certain formula involving the Laplace-Leray commutator. A key estimate of Liu et al. controls the commutator strictly by the Laplacian in energy norm at leading order. In this paper we show that this strict control fails in a large family of bounded planar domains with corners. However, when the domain is an infinite cone, we find that strict control may be recovered in certain power-law weighted norms.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-05T00:05:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal estimates",
      "laplace-leray commutator",
      "leray projection operator",
      "strict control fails",
      "bounded planar domains"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3958C"
    }
  }
}