# Global well-posedness of the MHD equations via the comparison principle

## TL;DR

This paper establishes the global well-posedness of the incompressible MHD equations near equilibrium in certain domains using the comparison principle and a comparison function.

## Contribution

It introduces a novel approach employing the comparison principle to prove global well-posedness for MHD equations in mixed domain settings.

## Key findings

- Proves global existence and uniqueness of solutions near equilibrium.
- Develops a new method based on the comparison principle.
- Applicable to domains of the form R^k x T^{d-k}.

## Abstract

In this paper, we prove the global well-posedness of the incompressible MHD equations near a homogeneous equilibrium in the domain $R^k\times T^{d-k}, d\geq2,k\geq1$ by using the comparison principle and constructing the comparison function.