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

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.