Sharp well-posedness for Kadomtsev–Petviashvili–Burgers (KPBII) equation in

We prove global well-posedness for the Cauchy problem associated with the Kadomtsev–Petviashvili–Burgers equation (KPBII) in when the initial value belongs to the anisotropic Sobolev space for all and s2 0. On the other hand, we prove in some sense that our result is sharp.