On global solutions and asymptotic behavior of planar magnetohydrodynamics with large data

Abstract

In this paper we consider an initial boundary value problem for planar magnetohydrodynamic compressible flows. By assuming that the adiabatic constant γ \gamma is sufficiently close to 1 1 , we prove the existence and uniqueness of global strong solutions with large initial data when all the viscosity, heat conductivity, and diffusivity coefficients are constant. Moreover, the asymptotic behavior of solutions is also investigated.