{
  "id": "2211.07808",
  "version": "v1",
  "published": "2022-11-15T00:30:18.000Z",
  "updated": "2022-11-15T00:30:18.000Z",
  "title": "Existence and Regularity for Vortex Patch Solutions of the 2D Euler Equations",
  "authors": [
    "Razvan-Octavian Radu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In \"Global regularity for vortex patches\" (Commun. Math. Phys. 1993), Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H\\\"older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-15T00:30:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35Q35",
      "76B47"
    ],
    "keywords": [
      "2d euler equations",
      "vortex patch solutions",
      "level-set framework",
      "vortex patch problem",
      "global regularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}