{
  "id": "2007.15758",
  "version": "v1",
  "published": "2020-07-30T22:12:24.000Z",
  "updated": "2020-07-30T22:12:24.000Z",
  "title": "Eulerian dynamics in multi-dimensions with radial symmetry",
  "authors": [
    "Changhui Tan"
  ],
  "comment": "34 pages, 6 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional Eulerian dynamics is the presence of the spectral gap, which is difficult to control in general. We propose a new pair of scalar quantities that provides a significant better control of the spectral gap. Two applications are presented. (i) the Euler-Poisson equations: we show a sharp threshold condition on initial data that distinguish global regularity and finite time blowup; (ii) the Euler-alignment equations: we show a large subcritical region of initial data that leads to global smooth solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-30T22:12:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35"
    ],
    "keywords": [
      "radial symmetry",
      "multi-dimensions",
      "initial data",
      "spectral gap",
      "significant better control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}