Sharp well-posedness for Kadomtsev–Petviashvili–Burgers (KPBII) equation in R2

We prove global well-posedness for the Cauchy problem associated with the Kadomtsev–Petviashvili–Burgers equation (KPBII) in R2 when the initial value belongs to the anisotropic Sobolev space Hs1,s2(R2) for all and s2⩾0. On the other hand, we prove in some sense that our result is sharp.