{
  "id": "1302.7084",
  "version": "v1",
  "published": "2013-02-28T05:00:58.000Z",
  "updated": "2013-02-28T05:00:58.000Z",
  "title": "Ill-posedness of the incompressible Navier-Stokes equations in $\\dot{F}^{-1,q}_{\\infty}({R}^3)$",
  "authors": [
    "C. Deng",
    "X. Yao"
  ],
  "comment": "19. arXiv admin note: text overlap with arXiv:1302.5785",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \\dot{F}^{-1,q}_{\\infty} (\\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data of $ \\dot{F}^{-1,q}_{\\infty}(\\mathbb{R}^3) $ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In view of the well-posedness of 3D-incompressible Navier-Stokes equations in $ BMO^{-1} $ (i.e. the Triebel-Lizorkin space $ \\dot{F}^{-1,2}_{\\infty}(\\mathbb{R}^3) $) by Koch and Tataru, our work completes a dichotomy of well-posedness and ill-posedness in the Triebel-Lizorkin space framework depending on $ q=2 $ or $ q>2 $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-28T05:00:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ill-posedness",
      "3d incompressible navier-stokes equations",
      "arbitrarily small initial data",
      "arbitrarily short time",
      "well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7084D"
    }
  }
}