This paper investigates the initial-boundary value problem (IBVP) of the planar magnetohydrodynamic equations with temperature dependent transport coefficients, that is, () =^, () =^ with 0, >0. In particular, the transverse magnetic field is assumed to satisfy the Neumann boundary condition, which was first investigated by Kazhikhov in 1987. We establish the global existence and uniqueness of strong solutions to the IBVP under some assumptions on the growth exponent. Furthermore, the nonlinear exponential stability of the global solutions is also obtained.
Tong et al. (Thu,) studied this question.