{
  "id": "math/0509096",
  "version": "v2",
  "published": "2005-09-05T13:40:16.000Z",
  "updated": "2005-11-25T16:22:07.000Z",
  "title": "On well-posedness for the Benjamin-Ono equation",
  "authors": [
    "N. Burq",
    "F. Planchon"
  ],
  "comment": "Important changes. We improved both existence and uniqueness results. In particular, uniqueness holds in the natural $L^\\infty_t; H^{1/2}_x$ energy space",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence of solutions for the Benjamin-Ono equation with data in $H^s(\\R)$, $s>0$. Thanks to conservation laws, this yields global solutions for $H^\\frac 1 2(\\R)$ data, which is the natural ``finite energy'' class. Moreover, inconditional uniqueness is obtained in $L^\\infty_t(H^\\frac 1 2(\\R))$, which includes weak solutions, while for $s>\\frac 3 {20}$, uniqueness holds in a natural space which includes the obtained solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-11-25T16:22:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "benjamin-ono equation",
      "well-posedness",
      "yields global solutions",
      "uniqueness holds",
      "weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......9096B"
    }
  }
}