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.