{
  "id": "1709.06077",
  "version": "v1",
  "published": "2017-09-15T19:18:23.000Z",
  "updated": "2017-09-15T19:18:23.000Z",
  "title": "Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces",
  "authors": [
    "Wei Yan",
    "Yongsheng Li",
    "Yimin Zhang"
  ],
  "comment": "38pages. arXiv admin note: substantial text overlap with arXiv:1709.01983",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Cauchy problem for the generalized KP-II equation \\begin{eqnarray*} u_{t}-|D_{x}|^{\\alpha}u_{x}+\\partial_{x}^{-1}\\partial_{y}^{2}u+\\frac{1}{2}\\partial_{x}(u^{2})=0,\\alpha\\geq4. \\end{eqnarray*} The goal of this paper is two-fold. Firstly, we prove that the problem is locally well-posed in anisotropic Sobolev spaces H^{s_{1},\\>s_{2}}(\\R^{2}) with s_{1}>\\frac{1}{4}-\\frac{3}{8}\\alpha, s_{2}\\geq 0 and \\alpha\\geq4. Secondly, we prove that the problem is globally well-posed in anisotropic Sobolev spaces H^{s_{1},\\>0}(\\R^{2}) with -\\frac{(3\\alpha-4)^{2}}{28\\alpha}<s_{1}\\leq0. and \\alpha\\geq4. Thus, our result improves the global well-posedness result of Hadac (Transaction of the American Mathematical Society, 360(2008), 6555-6572.) when 4\\leq \\alpha\\leq6.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-15T19:18:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anisotropic sobolev spaces",
      "generalized kp-ii equation",
      "global well-posedness result",
      "cauchy problem",
      "american mathematical society"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}