Sharp well-posedness for Kadomtsev-Petviashvili-Burgers (KPBII) equation in $R^2$

We prove global well-posedness for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers equation (KPBII) in ${\mathbb{R}}^2$ when the initial value belongs to the anisotropic Sobolev space $H^{s_1,s_2}(\mathbb R^2)$forall$s_1>-\frac12$and$s_2\geq0$. On the other hand, we prove in some sense that our result is sharp.