{
  "id": "1805.05229",
  "version": "v1",
  "published": "2018-05-14T15:28:03.000Z",
  "updated": "2018-05-14T15:28:03.000Z",
  "title": "The initial-boundary value problem for the Kawahara equation on the half-line",
  "authors": [
    "Márcio Cavalcante",
    "Chulkwang Kwak"
  ],
  "comment": "47 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper concerns the initial-boundary value problem (IBVP) of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing operator, which is introduced by Colliander - Kenig \\cite{CK} in the context of Airy group operators, to construct solutions on the whole line. We also give the bilinear estimate in $X^{s,b}$ space for $b < \\frac12$, which is almost sharp compared to IVP of Kawahara equation \\cite{CLMW2009, CG2011} (excluding only the endpoint regularity $s = -\\frac74$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-14T15:28:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53"
    ],
    "keywords": [
      "initial-boundary value problem",
      "kawahara equation",
      "low regularity sobolev space",
      "airy group operators",
      "duhamel boundary forcing operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}