Global well-posedness for the Kadomtsev-Petviashvili II equation

We study the global well-posedness of the Cauchy problem for the KP II equation. We prove the global well-posedness in the inhomogeneous-homogeneous anisotropicSobolev spaces Hx,y-1/78+ε,0∩ Hx,y-17/144,0.Though we require the use of the homogeneousSobolev space of negative index, we obtain the global well-posedness below L².