{
  "id": "2403.13691",
  "version": "v1",
  "published": "2024-03-20T15:54:39.000Z",
  "updated": "2024-03-20T15:54:39.000Z",
  "title": "Optimal Regularity for the 2D Euler Equations in the Yudovich class",
  "authors": [
    "Nicola de Nitti",
    "David Meyer",
    "Christian Seis"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We analyze the optimal regularity that is exactly propagated by a transport equation driven by a velocity field with BMO gradient. As an application, we study the 2D Euler equations in case the initial vorticity is bounded. The sharpness of our result for the Euler equations follows from a variation of Bahouri and Chemin's vortex patch example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-20T15:54:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "76B03",
      "76B47",
      "35B65"
    ],
    "keywords": [
      "2d euler equations",
      "optimal regularity",
      "yudovich class",
      "chemins vortex patch example",
      "transport equation driven"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}