{
  "id": "2411.18452",
  "version": "v1",
  "published": "2024-11-27T15:42:50.000Z",
  "updated": "2024-11-27T15:42:50.000Z",
  "title": "Self-similar instability and forced nonuniqueness: an application to the 2D Euler equations",
  "authors": [
    "Michele Dolce",
    "Giulia Mescolini"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Building on an approach introduced by Golovkin in the '60s, we show that nonuniqueness in some forced PDEs is a direct consequence of the existence of a self-similar linearly unstable eigenvalue: the key point is a clever choice of the forcing term removing complicated nonlinear interactions. We use this method to give a short and self-contained proof of nonuniqueness in 2D perfect fluids, first obtained in Vishik's groundbreaking result. In particular, we present a direct construction of a forced self-similar unstable vortex, where we treat perturbatively the self-similar operator in a new and more quantitative way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-27T15:42:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q31",
      "35Q35"
    ],
    "keywords": [
      "2d euler equations",
      "self-similar instability",
      "forced nonuniqueness",
      "application",
      "term removing complicated nonlinear interactions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}