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

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>max{1,gamma+2/4}, the density is shown to be uniformly bounded with respect to time. This generalizes the previous result [Fan et al., Arch. Ration. Mech. Anal. 245, 239-278 (2022)] of the compressible Navier-Stokes equations on 2D bounded domains where they require beta > 4/3 and also improves the result [Chen et al., SIAM J. Math. Anal. 54(3), 3817-3847 (2022)] of of compressible MHD equations on 2D solid balls.