{
  "id": "1606.00010",
  "version": "v1",
  "published": "2016-05-31T20:00:03.000Z",
  "updated": "2016-05-31T20:00:03.000Z",
  "title": "Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces",
  "authors": [
    "John Holmes",
    "Ryan C. Thompson"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1009.1820 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove well-posedness of the Fornberg-Whitham equation in Besov spaces $B_{2,r}^s$ in both the periodic and non-periodic cases. This will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data-to-solution map provided that the initial data belongs to $B_{2,r}^s $. We also establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from any bounded subset of $B_{2,r}^s$ to $C([-T,T]; B^s_{2,r})$. Furthermore, we prove a Cauchy-Kowalevski type theorem for this equation that establishes the existence and uniqueness of real analytic solutions and also provide blow-up criterion for solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-31T20:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53"
    ],
    "keywords": [
      "besov spaces",
      "fornberg-whitham equation",
      "continuity properties",
      "well-posedness",
      "data-to-solution map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}