Global strong solutions to the radially symmetric compressible MHD equations in 2D solid balls with arbitrary large initial data

Abstract

In this paper, we prove the global existence of strong solutions to the two-dimensional compressible MHD equations with density dependent viscosity coefficients (known as Kazhikhov-Vaigant model) on 2D solid balls with arbitrary large initial smooth data where shear viscosity $\mu$ being constant and the bulk viscosity $\lambda$ be a polynomial of density up to power $\beta$. The global existence of the radially symmetric strong solutions was established under Dirichlet boundary conditions for $\beta>1$. Moreover, as long as $\beta\in (\max\{1,\frac{\gamma+2}{4}\},\gamma]$, the density is shown to be uniformly bounded with respect to time. This generalizes the previous result of \cite{2022Li,2016Huang,2022Huang} of the compressible Navier-Stokes equations on 2D bounded domains where they require $\beta>4/3$ and also improves the result of \cite{chen2022,2015Mei-1,2015Mei-2} of compressible MHD equations on 2D solid balls.