Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 68, pp. 1-12.

Title: Global solution for the Kadomtsev-Petviashvili equation (KPII)
       in anisotropic Sobolev spaces of negative indices

Authors: Pedro Isaza J. (Univ. Nacional de Colombia, Medellin, Colombia)
 Jorge Mejia L.  (Univ. Nacional de Colombia, Medellin, Colombia)

Abstract: 
 It is proved that the Cauchy problem for the Kadomtsev-Petviashvili
 equation (KPII) is globally well-posed for initial data in anisotropic
 Sobolev spaces $H^{s0}(\mathbb{R}^2)$ with $s>-1/14$.
 The extension of a local solution to a solution in an arbitrary interval
 is carried out by means of an almost conservation property of the 
 $H^{s0}$ norm of the solution.
 
Submitted September 13, 2002. Published June 13, 2003.
Math Subject Classifications: 35Q53, 37K05.
Key Words: Nonlinear dispersive equations; global solutions; 
           almost conservation laws.