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

Abstract

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 Hs1 , s2 (ℝ2) with s1 > -5/4 and s2 ≥ 0, and globally well-posed in Hs,0 (ℝ2) s >-4/7.