{
  "id": "1909.07314",
  "version": "v1",
  "published": "2019-09-16T16:18:17.000Z",
  "updated": "2019-09-16T16:18:17.000Z",
  "title": "On the flow map of the Benjamin-Ono equation on the torus",
  "authors": [
    "Patrick Gerard",
    "Thomas Kappeler",
    "Peter Topalov"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that for any $t\\in\\mathbb{R}$, the flow map $\\mathcal{S}^t$ of the Benjamin-Ono equation on the torus continuously extends to the Sobolev space $H^{-s}_{r,0}$ for any $0<s<1/2$, but does not do so to $H^{-s}_{r,0}$ for $s>1/2$. Furthermore, we show that $\\mathcal{S}^t$ is sequentially weakly continuous on $H^{-s}_{r,0}$ for any $0\\le s<1/2$. Note that $- 1/2$ is the critical Sobolev exponent of the Benjamin-Ono equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-16T16:18:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "benjamin-ono equation",
      "flow map",
      "sobolev space",
      "critical sobolev exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}