{
  "id": "0904.2196",
  "version": "v1",
  "published": "2009-04-14T20:14:46.000Z",
  "updated": "2009-04-14T20:14:46.000Z",
  "title": "Ill-posedness of basic equations of fluid dynamics in Besov spaces",
  "authors": [
    "A. Cheskidov",
    "R. Shvydkoy"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We give a construction of a divergence-free vector field $u_0 \\in H^s \\cap B^{-1}_{\\infty,\\infty}$, for all $s<1/2$, such that any Leray-Hopf solution to the Navier-Stokes equation starting from $u_0$ is discontinuous at $t=0$ in the metric of $B^{-1}_{\\infty,\\infty}$. For the Euler equation a similar result is proved in all Besov spaces $B^s_{r,\\infty}$ where $s>0$ if $r>2$, and $s>n(2/r-1)$ if $1 \\leq r \\leq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-14T20:14:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "35Q30"
    ],
    "keywords": [
      "besov spaces",
      "fluid dynamics",
      "basic equations",
      "ill-posedness",
      "divergence-free vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.2196C"
    }
  }
}