{
  "id": "2403.12824",
  "version": "v1",
  "published": "2024-03-19T15:28:27.000Z",
  "updated": "2024-03-19T15:28:27.000Z",
  "title": "Well-posedness and no-uniform dependence for the Euler-Poincaré equations in Triebel-Lizorkin spaces",
  "authors": [
    "Yuanhua Zhong",
    "Jianzhong Lu",
    "Min Li",
    "Jinlu Li"
  ],
  "comment": "17pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study the Cauchy problem of the Euler-Poincar\\'{e} equations in $\\R^d$ with initial data belonging to the Triebel-Lizorkin spaces. We prove the local-in-time unique existence of solutions to the Euler-Poincar\\'{e} equations in $F^s_{p,r}(\\R^d)$. Furthermore, we obtain that the data-to-solution of this equation is continuous but not uniformly continuous in these spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-19T15:28:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35"
    ],
    "keywords": [
      "triebel-lizorkin spaces",
      "no-uniform dependence",
      "well-posedness",
      "local-in-time unique existence",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}