{
  "id": "1810.07993",
  "version": "v1",
  "published": "2018-10-18T11:28:36.000Z",
  "updated": "2018-10-18T11:28:36.000Z",
  "title": "Blow-up phenomenon, ill-posedness and peakon solutions for the periodic Euler-Poincaré equations",
  "authors": [
    "Wei Luo",
    "Zhaoyang Yin"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we mainly investigate the initial value problem of the periodic Euler-Poincar\\'e equations. We first present a new blow-up result to the system for a special class of smooth initial data by using the rotational invariant properties of the system. Then, we prove that the periodic Euler-Poincar\\'e equations is ill-posed in critical Besov spaces by a contradiction argument. Finally, we verify the system possesses a class of peakon solutions in the sense of distributions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-18T11:28:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "peakon solutions",
      "blow-up phenomenon",
      "periodic euler-poincare equations",
      "ill-posedness",
      "rotational invariant properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}