Abstract: | In this paper, we study the isentropic compressible planar magnetohydrodynamic equations with viscosity depending on density and with free boundaries. Precisely, when the viscosity coefficient λ(ρ) is proportional to ρθ with θ > 0, where ρ is the density, we establish the existence of global solutions under certain assumptions on the initial data by deriving some new a priori estimates. |