{
  "id": "0905.0039",
  "version": "v1",
  "published": "2009-05-01T02:58:32.000Z",
  "updated": "2009-05-01T02:58:32.000Z",
  "title": "On the local regularity of the KP-I equation in anisotropic Sobolev space",
  "authors": [
    "Zihua Guo",
    "Lizhong Peng",
    "Baoxiang Wang"
  ],
  "comment": "23 pages, 0 figures, submitted",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that the KP-I initial-value problem \\begin{eqnarray*} \\begin{cases} \\partial_tu+\\partial_x^3u-\\partial_x^{-1}\\partial_y^2u+\\partial_x(u^2/2)=0 {on}{\\R}^2_{x,y}\\times {\\R}_t; u(x,y,0)=\\phi(x,y), \\end{cases} \\end{eqnarray*} is locally well-posed in the space \\begin{eqnarray*} H^{1,0}(\\R^2)=\\{\\phi\\in L^2(\\R^2): \\ \\norm{\\phi}_{H^{1,0}(\\R^2)}\\approx\\norm{\\phi}_{L^2}+\\norm{\\partial_x\\phi}_{L^2}<\\infty\\}. \\end{eqnarray*}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-01T02:58:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anisotropic sobolev space",
      "kp-i equation",
      "local regularity",
      "kp-i initial-value problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}