Abstract:

In this paper, we are concerned with the the global existence and non-linear stability of the compressible and radiative Navier-Stokes matrixs when the viscosity $\lambda$ and heat conductivity $\kappa$ depend on temperature $\theta$, i.e., $\lambda(\theta)=\theta^\alpha$, $\kappa(\theta)=1+\theta^\beta$ with $\alpha \in [0, +\infty)$, $\beta \in (2, +\infty)$. The global existence and uniqueness of strong solutions are obtained under the assumptions on the parameter $\alpha$ and initial data. In addition, we also proved the non-linear exponential stability of the solutions on the basis of the fundamental uniform-in-time estimates. It should be note that the initial data could be large if $\alpha$ is small and the growth exponent $\beta$ can be arbitrarily large.

Key words: Compressible Navier-Stokes matrixs, Thermal radiation, Temperature-dependent transport coefficients, Large initial data, Global solutions