# American Institute of Mathematical Sciences

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

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

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