Global well-posedness for the Kadomtsev-Petviashvili II equation

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April 2000, 6(2): 483-499. doi: 10.3934/dcds.2000.6.483

Global well-posedness for the Kadomtsev-Petviashvili II equation

1.	Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro 153-8914 Tokyo, Japan

Received February 1999 Revised May 1999 Published January 2000

Abstract
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We study the global well-posedness of the Cauchy problem for the KP II equation. We prove the global well-posedness in the inhomogeneous-homogeneous anisotropic Sobolev spaces $H_{x,y}^{-1/78+\epsilon,0}\cap H_{x,y}^{-17/144,0}$. Though we require the use of the homogeneous Sobolev space of negative index, we obtain the global well-posedness below $L^2$.

Keywords: well-posedness., anisotropic Sobolev spaces, KP equations.

Mathematics Subject Classification: 35Q5.

Citation: Hideo Takaoka. Global well-posedness for the Kadomtsev-Petviashvili II equation. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 483-499. doi: 10.3934/dcds.2000.6.483

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