{
  "id": "0807.2193",
  "version": "v1",
  "published": "2008-07-14T16:30:27.000Z",
  "updated": "2008-07-14T16:30:27.000Z",
  "title": "Well-posedness for the generalized Benjamin-Ono equations with arbitrary large initial data in the critical space",
  "authors": [
    "Stéphane Vento"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the generalized Benjamin-Ono equations $\\partial_tu+\\mathcal{H}\\partial_x^2u\\pm u^k\\partial_xu=0$, $k\\geq 4$ are locally well-posed in the scaling invariant spaces $\\dot{H}^{s_k}(\\R)$ where $s_k=1/2-1/k$. Our results also hold in the non-homogeneous spaces $H^{s_k}(\\R)$. In the case $k=3$, local well-posedness is obtained in $H^{s}(\\R)$, $s>1/3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-14T16:30:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B30",
      "76B03",
      "76B55"
    ],
    "keywords": [
      "arbitrary large initial data",
      "generalized benjamin-ono equations",
      "critical space",
      "scaling invariant spaces",
      "local well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2193V"
    }
  }
}