Global existence of strong solutions to the compressible magnetohydrodynamic equations with large initial data and vacuum in R2

Abstract

This paper concerns the Cauchy problem to the compressible magnetohydrodynamic equations in $R^2$ with the constant state of density at far field being vacuum or nonvacuum. Under the conditions that the adiabatic constant $\gamma >1$, the shear viscosity coefficient μ is a positive constant, and the bulk one $\lambda \left(\rho \right)={\rho }^{\beta }$ with $\beta >4/3$, we establish the global existence and uniqueness of strong solutions. In particular, the initial data can be arbitrarily large and the density is allowed to vanish initially. These results generalize and improve previous ones by Huang-Li (2022) and Jiu-Wang-Xin (2018) for compressible Navier-Stokes equations. This paper introduces some key weighted estimates on H and presents some delicate analysis to exploit the decay properties of solutions due to the strong coupling and interplay interaction.