Electron. J. Diff. Eqns., Vol. 2003(2003), No. 68, pp. 1-12.

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

Pedro Isaza J. & Jorge Mejia L.

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 $s greater than -1/14$. 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.

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Pedro Isaza J.
Escuela de Matematicas
Universidad Nacional de Colombia
A. A. 3840 Medellin, Colombia
email: pisaza@perseus.unalmed.edu.co
Jorge Mejia L.
Escuela de Matematicas
Universidad Nacional de Colombia
A. A. 3840 Medellin, Colombia
email: jemejia@perseus.unalmed.edu.co

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