# Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

## TL;DR

This paper investigates the 2D MHD-Boussinesq system with stratification effects, establishing global weak and strong solutions, and demonstrating exponential decay under certain conditions.

## Contribution

It provides the first comprehensive analysis of global solutions for the 2D MHD-Boussinesq system with temperature-dependent properties and stratification effects.

## Key findings

- Existence of global weak solutions under minimal initial assumptions.
- Existence and uniqueness of global strong solutions with higher regularity.
- Exponential decay rate of solutions over time.

## Abstract

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay estimate of the solution is obtained.