{
  "id": "2301.03383",
  "version": "v1",
  "published": "2022-11-09T08:22:57.000Z",
  "updated": "2022-11-09T08:22:57.000Z",
  "title": "On the continuity of the solution map of the Euler-Poincaré equations in Besov spaces",
  "authors": [
    "Min Li"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "By constructing a series of perturbation functions through localization in the Fourier domain and translation, we show that the data-to-solution map for the Euler-Poincar\\'e equations is nowhere uniformly continuous in $B^s_{p,r}(\\mathbb{R} ^d)$ with $s>\\max\\{1+\\frac d2,\\frac32\\}$ and $(p,r)\\in (1,\\infty)\\times [1,\\infty)$. This improves our previous result which shows the data-to-solution map for the Euler-Poincar\\'e equations is non-uniformly continuous on a bounded subset of $B^s_{p,r}(\\mathbb{R} ^d)$ near the origin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-09T08:22:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35Q51",
      "35L30"
    ],
    "keywords": [
      "besov spaces",
      "continuity",
      "euler-poincare equations",
      "data-to-solution map",
      "fourier domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}