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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

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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