Global classical solutions to the 1D compressible non-resistive magnetohydrodynamic equations with density-dependent viscosity

In this paper, we are concerned with the one-dimensional initial-boundary value problem of the compressible non-resistive magnetohydrodynamic system with density-dependent viscosity. Without any constraint between the initial density and the initial magnetic field as needed in Yu [Acta Appl. Math. 128, 193–209 (2013)], we show the global existence of classical solutions to the problem for general large initial data that allow for initial vacuum. Moreover, we derive the uniform-in-time upper bounds for both the density function and the magnetic field, and then show the large-time behavior of the velocity.