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Global well-posedness for the Kadomtsev-Petviashvili II equation. (English) Zbl 1021.35099

The author studies well-posedness of the following Cauchy problem for the Kadomtsev-Petviashvili II equation: \[ \begin{aligned} & \partial_x(\partial_t u+\partial^3_x u+\partial_x(u^2))+\partial^2_y u=0,\;(t,x,y)\in\mathbb{R}^3,\\ & u(0,x,y)=u+0(x,y),\quad (x,y)\in\mathbb{R}^2.\end{aligned} \] The author proves the global well-posedness in the inhomogeneous-homogeneous anisotropic Sobolev spaces \(H^{-1/78+\varepsilon,0}_{x,y}\cap \dot H^{-17/144,0}_{x,y}\).

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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