{
  "id": "0709.0103",
  "version": "v2",
  "published": "2007-09-02T11:51:02.000Z",
  "updated": "2008-05-15T02:49:59.000Z",
  "title": "On the low regularity of the fifth order Kadomtsev-Petviashvili I equation",
  "authors": [
    "Wengu Chen",
    "Junfeng Li",
    "Changxing Miao"
  ],
  "comment": "30pages",
  "journal": "J. Differential Equations 245 (2008) 3433-3469",
  "doi": "10.1016/j.jde.2008.07.005",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the fifth order Kadomtsev-Petviashvili I (KP-I) equation as $\\partial_tu+\\alpha\\partial_x^3u+\\partial^5_xu+\\partial_x^{-1}\\partial_y^2u+uu_x=0,$ while $\\alpha\\in \\mathbb{R}$. We introduce an interpolated energy space $E_s$ to consider the well-posedeness of the initial value problem (IVP) of the fifth order KP-I equation. We obtain the local well-posedness of IVP of the fifth order KP-I equation in $E_s$ for $0<s\\leq1$. To obtain the local well-posedness, we present a bilinear estimate in the Bourgain space in the framework of the interpolated energy space. It crucially depends on the dyadic decomposed Strichartz estimate, the fifth order dispersive smoothing effect and maximal estimate. Key words: The fifth order KP-I equation, Bourgain space, Dyadic decomposed Strichartz estimate, Dispersive smoothing effect, Maximal estimate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-15T02:49:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q53",
      "35G25"
    ],
    "keywords": [
      "fifth order kadomtsev-petviashvili",
      "fifth order kp-i equation",
      "low regularity",
      "dyadic decomposed strichartz estimate",
      "order dispersive smoothing effect"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2008,
      "volume": 245,
      "number": 11,
      "pages": 3433
    },
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JDE...245.3433C"
    }
  }
}