The Cauchy problem for the DMKP equation

TL;DR

This paper investigates the well-posedness of the dissipation-modified Kadomtsev-Petviashvili (DMKP) equation in two dimensions, establishing local and global solutions in anisotropic Sobolev spaces and demonstrating the sharpness of these results.

Contribution

It proves local and global well-posedness of the DMKP equation in anisotropic Sobolev spaces, showing the results are sharp and extending understanding of this PDE.

Findings

Local well-posedness in anisotropic Sobolev spaces

Global well-posedness under certain conditions

Results are sharp in the context of the equation's properties

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.