The Cauchy problem for the dissipation-modified Kadomtsev–Petviashvili equation

Considered herein is the dissipation-modified Kadomtsev–Petviashvili equation in two space-dimensional case. It is established that the Cauchy problem associated to this equation is locally well-posed in anisotropic Sobolev spaces. It is also shown in some sense that this result is sharp. In addition, the global well-posedness for this equation under suitable conditions is proved.