{
  "id": "1511.02207",
  "version": "v1",
  "published": "2015-11-06T19:40:56.000Z",
  "updated": "2015-11-06T19:40:56.000Z",
  "title": "Ill-posedness for the BBM equation in $H^s$ with $s<0$",
  "authors": [
    "Jerry Bona",
    "Mimi Dai"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the ill-posedness problem for the regularized long-wave equation (Benjamin-Bona-Mahony equation) in the Sobolev space $H^s$ with $s<0$. It is shown that the solution map in $H^s$ is discontinuous at the origin. More precisely, we construct an arbitrarily small initial data such that the solution becomes arbitrarily large instantaneously in $H^s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-06T19:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "35Q35"
    ],
    "keywords": [
      "bbm equation",
      "arbitrarily small initial data",
      "regularized long-wave equation",
      "benjamin-bona-mahony equation",
      "solution map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102207B"
    }
  }
}