{
  "id": "1405.1943",
  "version": "v1",
  "published": "2014-05-08T14:34:49.000Z",
  "updated": "2014-05-08T14:34:49.000Z",
  "title": "Ill-posedness of the incompressible Euler equations in the $C^1$ space",
  "authors": [
    "Gerard Misiołek",
    "Tsuyoshi Yoneda"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the 2D Euler equations are not locally well-posed in $C^1$. Our approach relies on the technique of Lagrangian deformations and norm inflation of Bourgain and Li. We show that the assumption that the data-to-solution map is continuous in $C^1$ leads to a contradiction with a well-posedness result in $W^{1,p}$ of Kato and Ponce.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-08T14:34:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "incompressible euler equations",
      "ill-posedness",
      "2d euler equations",
      "well-posedness result",
      "lagrangian deformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.1943M"
    }
  }
}