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Global well-posedness of the Cauchy problem for a fifth-order KP-I equation in anisotropic Sobolev spaces
Yongsheng Li, Wei Yan, Yimin Zhang
In this paper, we consider the Cauchy problem for the fifth-order KP-I equation \begin{align*} u_t + \partial_x^5u+\partial_x^{-1}\partial_y^2u + \frac{1}{2}\partial_x(u^2)=0. \end…
math.AP2017
Global well-posedness of the generalized KP-II equation in anisotropic Sobolev spaces
Wei Yan, Yongsheng Li, Yimin Zhang
In this paper, we consider the Cauchy problem for the generalized KP-II equation \begin{eqnarray*} u_{t}-|D_{x}|^αu_{x}+\partial_{x}^{-1}\partial_{y}^{2}u+\frac{1}{2}\partial_{x}(u…