Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum

TL;DR

This paper proves the global existence and uniqueness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum, extending previous results for the Navier-Stokes equations.

Contribution

It establishes the global well-posedness of classical solutions for the 2D compressible MHD equations with large data and vacuum, under specific viscosity assumptions, on both the torus and the whole space.

Findings

Global classical solutions exist and are unique.

Results apply to both torus and Euclidean space.

Generalizes previous Navier-Stokes results.

Abstract

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption $\mu=const.$ and $\lambda=\rho^\beta,~\beta>1$ (Va\v{i}gant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus $\mathbb{T}^2$ and the whole space $\mathbb{R}^2$ (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Va\v{i}gant-Kazhikhov model of compressible Navier-Stokes.