Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients - Mingyu Zhang (Axioms)
The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity <semantics>λ</semantics> and heat conductivity <semantics>κ</semantics> depend on temperature, i.e., <semantics>λ=θα</semantics> and <semantics>κ=θβ</semantics> with <semantics>α,β∈[0,+∞)</semantics>. Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter <semantics>α</semantics> and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if <semantics>α</semantics> is small and the growth exponent <semantics>β</semantics> can be arbitrarily large.