{
  "id": "math/9911223",
  "version": "v2",
  "published": "1999-11-29T17:07:02.000Z",
  "updated": "2000-07-10T17:19:01.000Z",
  "title": "Finite time blow up for a Navier-Stokes like equation",
  "authors": [
    "Stephen Montgomery-Smith"
  ],
  "comment": "Also available at http://www.math.missouri.edu/~stephen/preprints/",
  "journal": "Proc. A.M.S., 129, (2001), 3017-3023",
  "categories": [
    "math.AP",
    "math-ph",
    "math.CA",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We consider an equation similar to the Navier-Stokes equation. We show that there is initial data that exists in every Triebel-Lizorkin or Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the solution is in no Triebel-Lizorkin or Besov space (and hence in no Lebesgue or Sobolev space). The purpose is to show the limitations of the so called semigroup method for the Navier-Stokes equation. We also consider the possibility of existence of solutions with initial data in the Besov space $\\dot B^{-1,\\infty}_\\infty$. We give initial data in this space for which there is no reasonable solution for the Navier-Stokes like equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-07-10T17:19:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "46E35",
      "34G20",
      "37L05",
      "47D06",
      "47H10"
    ],
    "keywords": [
      "finite time blow",
      "besov space",
      "initial data",
      "navier-stokes equation",
      "sobolev space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11223M"
    }
  }
}