{
  "id": "1405.2478",
  "version": "v3",
  "published": "2014-05-10T22:52:25.000Z",
  "updated": "2017-07-15T18:37:04.000Z",
  "title": "Ill-posedness results in critical spaces for some equations arising in hydrodynamics",
  "authors": [
    "Tarek M. Elgindi",
    "Nader Masmoudi"
  ],
  "comment": "Fixed some typos. Fixed an error in the proof of Proposition 3.1. Added a short section on the Euler equations in $C^k$",
  "categories": [
    "math.AP"
  ],
  "abstract": "Many questions related to well-posedness/ill-posedness in critical spaces for hydrodynamic equations have been open for many years. Some of them have only recently been settled. In this article we give a new approach to studying norm inflation (in some critical spaces) for a wide class of equations arising in hydrodynamics. As an application, we prove strong ill-posedness of the $d$-dimensional Euler equations in the class $C^1\\cap L^2.$ We give two proofs of this result in sections 8 and 9.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-24T19:33:15.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-07-15T18:37:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical spaces",
      "equations arising",
      "ill-posedness results",
      "dimensional euler equations",
      "wide class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2478E"
    }
  }
}