{
  "id": "1901.11432",
  "version": "v1",
  "published": "2019-01-31T15:39:34.000Z",
  "updated": "2019-01-31T15:39:34.000Z",
  "title": "Uniqueness Properties of Solutions to the Benjamin-Ono equation and related models",
  "authors": [
    "Carlos E. Kenig",
    "Gustavo Ponce",
    "Luis Vega"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that if $u_1,\\,u_2$ are solutions of the Benjamin-Ono equation defined in $ (x,t)\\in\\R \\times [0,T]$ which agree in an open set $\\Omega\\subset \\R \\times [0,T]$, then $u_1\\equiv u_2$. We extend this uniqueness result to a general class of equations of Benjamin-Ono type in both the initial value problem and the initial periodic boundary value problem. This class of 1-dimensional non-local models includes the intermediate long wave equation. Finally, we present a slightly stronger version of our uniqueness results for the Benjamin-Ono equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-31T15:39:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "benjamin-ono equation",
      "uniqueness properties",
      "related models",
      "initial periodic boundary value problem",
      "intermediate long wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}