Large-time behavior of cylindrically symmetric Navier-Stokes equations with temperature-dependent viscosity and heat conductivity

In this study, the initial-boundary value problem for cylindrically symmetric Navier-Stokes equations was considered with temperature-dependent viscosity and heat conductivity. Firstly, we established the existence and uniqueness of a strong solution when the viscosity and heat conductivity were both power functions of temperature. Moreover, the large-time behavior of the strong solution was obtained with large initial data, since all of the estimates in this paper were independent of time. It is worth noting that we identified the relationship between the initial data and the power of the temperature in the viscosity for the first time.