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

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December 2006, 5(4): 887-905. doi: 10.3934/cpaa.2006.5.887

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

Pedro Isaza ^1, , Juan López ^2, and Jorge Mejía ^1,

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

Received November 2005 Revised March 2006 Published September 2006

Abstract
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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 $s$>$-\frac{4}{7}.$

Keywords: Nonlinear dispersive equations, local solutions, global solutions..

Mathematics Subject Classification: Primary: 35Q53; Secondary: 37K0.

Citation: Pedro Isaza, Juan López, Jorge Mejía. Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation. Communications on Pure & Applied Analysis, 2006, 5 (4) : 887-905. doi: 10.3934/cpaa.2006.5.887

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