Global symmetric classical solutions for radiative compressible Navier-Stokes equations with temperature-dependent viscosity coefficients

This paper is concerned with the global solvability and the precise description of large time behavior of global solutions to the compressible viscous and heat-conducting ideal polytropic gases in a bounded concentric annular domain with radiation and temperature-dependent viscosity. For the case that the transport coefficients are smooth functions of temperature, a unique global-in-time spherically or cylindrically symmetric classical solution to the above initial-boundary value problem is shown to exist and decay into a constant equilibrium state at exponential rate as the time variable tends to infinity. In our results, the initial data can be large if the adiabatic exponent is sufficiently close to 1.