The Cauchy problem for the DMKP equation

Abstract

In this work, we study the dissipation-modified Kadomtsev-Petviashvili equation in two space-dimensional case. We establish that the Cauchy problem for this equation is locally well-posed in anisotropic Sobolev spaces. We show in some sense that our result is sharp. We also prove the global well-posedness for this equation under suitable conditions.

19 pages. Submitted