{"paper":{"title":"Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Yan, Yimin Zhang, Yongsheng Li","submitted_at":"2017-09-15T19:18:23Z","abstract_excerpt":"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}