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.