On the well-posedness for Kadomtsev–Petviashvili–Burgers I equation

We prove local and global well-posedness in Hs,0(R2), , for the Cauchy problem associated with the Kadomtsev–Petviashvili–Burgers I equation (KPBI) by working in Bourgainʼs type spaces. This result is almost sharp if one requires the flow-map to be smooth.