Large-Time Behavior of Global Solutions to the Cauchy Problem of the Planar Compressible Magnetohydrodynamic Equations

Abstract

There have already been some results concerning on the global existence of solutions to the Cauchy problem of the planar compressible magnetohydrodynamic equations with large initial data. However, few results have focused on its large-time behavior. The main purpose of this paper is to study the large-time behavior of global solutions to the Cauchy problem of the above system. The viscosity can be a positive constant or density-dependent. The key point in our analysis is to derive the uniform-in-time positive lower and upper bounds on the specific volume and the absolute temperature. Moreover, the interaction between the hydrodynamics and magnetodynamic effects has also been dealt with properly.