{
  "id": "math/0609781",
  "version": "v2",
  "published": "2006-09-28T05:44:35.000Z",
  "updated": "2007-01-24T15:27:40.000Z",
  "title": "Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO^{-1}",
  "authors": [
    "Pierre Germain",
    "Nataša Pavlović",
    "Gigliola Staffilani"
  ],
  "comment": "32 pages, a proof of spatial analyticity included, a regularity result for the self-similar solutions added",
  "categories": [
    "math.AP"
  ],
  "abstract": "In 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ${\\mathbb{R}}^d$ for initial data small enough in $BMO^{-1}$. We show in this article that the Koch and Tataru solution has higher regularity. As a consequence, we get a decay estimate in time for any space derivative, and space analyticity of the solution. Also as an application of our regularity theorem, we prove a regularity result for self-similar solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-24T15:27:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "navier-stokes equations evolving",
      "small data",
      "initial data small",
      "higher regularity",
      "regularity result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9781G"
    }
  }
}