{
  "id": "2210.17458",
  "version": "v1",
  "published": "2022-10-31T16:31:31.000Z",
  "updated": "2022-10-31T16:31:31.000Z",
  "title": "Instantaneous gap loss of Sobolev regularity for the 2D incompressible Euler equations",
  "authors": [
    "Diego Córdoba",
    "Luis Martínez-Zoroa",
    "Wojciech Ozanski"
  ],
  "comment": "28 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct solutions of the 2D incompressible Euler equations in $\\mathds{R}^2\\times [0,\\infty)$ such that initially the velocity is in the super-critical Sobolev space $H^\\beta$ for $1<\\beta<2$, but are not in $H^{\\beta'}$ for $\\beta'>1+\\frac{(3-\\beta)(\\beta-1)}{2 - (\\beta-1)^2}$ for $0<t<\\infty$. These solutions are not in the Yudovich class, but they exists globally in time and they are unique in a determined family of classical solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-31T16:31:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "2d incompressible euler equations",
      "instantaneous gap loss",
      "sobolev regularity",
      "yudovich class",
      "construct solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}