{
  "id": "2204.13406",
  "version": "v1",
  "published": "2022-04-28T10:50:14.000Z",
  "updated": "2022-04-28T10:50:14.000Z",
  "title": "On the regularity of axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions",
  "authors": [
    "Evan Miller"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we will discuss the axisymetric, swirl-free Euler equation in four and higher dimensions. We will show that in four and higher dimensions the axisymetric, swirl-free Euler equation has properties which could allow finite-time singularity formation of a form that is excluded in three dimensions. We will also consider a model equation that is obtained by taking the infinite-dimensional limit of the vorticity equation in this setup. This model exhibits finite-time blowup of a Burgers shock type. The blowup result for the infinite dimensional model equation heavily suggests that smooth solutions of the Euler equation exhibit finite-time blowup in sufficiently high dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-28T10:50:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "76B47"
    ],
    "keywords": [
      "higher dimensions",
      "swirl-free solutions",
      "swirl-free euler equation",
      "regularity",
      "axisymmetric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}