Global well-posedness for the Kadomtsev-Petviashvili II equation

Hideo Takaoka

doi:10.3934/dcds.2000.6.483

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2000, Volume 6, Issue 2: 483-499. Doi: 10.3934/dcds.2000.6.483

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Global well-posedness for the Kadomtsev-Petviashvili II equation

Hideo Takaoka^1,

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

Received: January 31, 1999

Revised: April 30, 1999

Published: March 2000

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Abstract

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 $L^2$.

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Mathematics Subject Classification: 35Q53.

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