On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation
  We prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s > -1/2$, for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers-I equation (KPBI) by working in Bourgain's type spaces. This result is almost sharp if one requires the flow-map to be smooth. 
Mohamad Darwich (LMPT)
math.AP