Global weak solutions and incompressible limit to the isentropic compressible magnetohydrodynamic equations in 2D bounded domains with ripped density and large initial data

TL;DR

This paper extends previous results on global weak solutions and incompressible limits of 2D isentropic compressible magnetohydrodynamic equations to bounded convex domains with Navier-slip boundary conditions, providing uniform estimates.

Contribution

It generalizes prior work from the whole plane to bounded domains, establishing uniform a priori estimates independent of bulk viscosity.

Findings

Established global weak solutions in bounded convex domains.

Proved incompressible limit under Navier-slip boundary conditions.

Obtained uniform a priori estimates independent of viscosity.

Abstract

In our previous work (arXiv:2510.00812), we have shown the global existence and incompressible limit of weak solutions to the isentropic compressible magnetohydrodynamic equations involving ripped density and large initial energy in the whole plane. In this paper we generalize such results to the case of two-dimensional bounded convex domains under Navier-slip boundary conditions. When comparing to the known results for global solutions of the initial-boundary value problem, we obtain uniform a priori estimates independent of the bulk viscosity coefficient.