Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

Pedro Isaza; Juan López; Jorge Mejía

doi:10.3934/cpaa.2006.5.887

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2006, Volume 5, Issue 4: 887-905. Doi: 10.3934/cpaa.2006.5.887

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Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

1.
Universidad Nacional de Colombia, Sede Medellín, A.A. 3840, Medellín
2.
Universidad de Pamplona, Pamplona

Received: October 31, 2005

Revised: February 28, 2006

Published: November 2006

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Abstract

It is proved that the initial value problem for the fifth order Kadomtsev-Petviashvili (KPII) equation is locally well-posed in the anisotropic Sobolev spaces $H^{s_1,s_2}( \mathbb R^2) $ with $s_1$>$-\frac{5}{4}$ and $s_2\geq 0,$ and globally well-posed in $H^{s,0}(\mathbb R^2) $ with $s$>$-\frac{4}{7}.$

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 37K05.

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Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

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