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

Abstract

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 $H^{s_1,s_2}(\mathbb R^2)$ for all $s_1>-\frac12$ and $s_2\geq0$. On the other hand, we prove in some sense that our result is sharp.