Global Wellposedness Of Magnetohydrodynamics System With Temperature-Dependent Viscosity

Fluid motion is the most common form of motion in nature.Describing and recognizing its rule is a basic problem in fluid dynamics theory.The motion of general fluid is very com-plex,which usually contain viscosity and elasticity.If the fluid has no elastic deformation,the mathematical equation describing its motion is the basic fluid equation.And the model describing the motion state of conducting fluid in magnetic field is called the magnetohydro-dynamics(MHD)system,and the research of MHD system has a lot of practical application in astrophysics,plasma physics and so on.The MHD system can be derived from the laws of fluid dynamics and the electromagnetism theory of Maxwell.Due to the interaction of fluid and magnetic field,and the strong coupling effect between them,the mathematical structure and dynamical mechanism of the MHD system are considerably complicated.We consider the initial boundary value problem of the one-dimensional MHD system when the viscosity,thermal conductivity,and magnetic diffusion coefficients are general differentiable functions of temperature with high order in this paper.A unique global classical solution is shown to exist uniquely and converge to the constant state as the time tends to infinity under certain assumptions on the initial data and the adiabatic exponent ?,and the initial data can be large if ? is sufficiently close to 1.