{
  "id": "1412.8407",
  "version": "v3",
  "published": "2014-12-29T18:02:46.000Z",
  "updated": "2015-04-14T13:08:55.000Z",
  "title": "On well-posedness of parabolic equations of Navier-Stokes type with BMO^{-1}(\\R^n) data",
  "authors": [
    "Pascal Auscher",
    "Dorothee Frey"
  ],
  "comment": "Second revision. Addition of 9 pages. Statement and proof of a corresponding linear PDE and proofs that we obtain indeed weak solutions",
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop a strategy making extensive use of tent spaces to study parabolic equa-tions with quadratic nonlinearities as for the Navier-Stokes system. We begin with a new proof of the well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in \\R^n with small initial data in BMO^{-1}(\\R^n). We then study another model where neither pointwise kernel bounds nor self-adjointness are available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-29T18:02:46.000Z",
      "abstract": "We develop a strategy making extensive use of tent spaces to study parabolic equa-tions with quadratic nonlinearities as for the Navier-Stokes system. We begin with a new proof of the well-known result of Koch and Tataru on the well-posedness of Navier-Stokes equations in \\R^n with small initial data in BMO^{-1}(\\R^n). We then study another model where neither pointwise kernel bounds nor self-adjointness are available. In this case, BMO^{-1}(\\R^n) has to be replaced by an adapted space.",
      "comment": "This article subsumes and replaces a previous deposit arXiv:1310.3783 by the same authors called \"A new proof for Koch and Tataru's result on the well-posedness of Navier-Stokes equations in $BMO^{-1}$\". We included another model to which a suitable modification of our proof for Navier-Stokes can be employed",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-04-14T13:08:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q10",
      "76D05",
      "42B37",
      "42B35"
    ],
    "keywords": [
      "parabolic equations",
      "navier-stokes type",
      "well-posedness",
      "study parabolic equa-tions",
      "small initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8407A"
    }
  }
}