Nonlinearly exponential stability for the compressible Navier-Stokes equations with temperature-dependent transport coefficients.

This paper is concerned with an initial and boundary value problem of the compressible Navier-Stokes equations for one-dimensional viscous and heat-conducting ideal polytropic fluids with temperature-dependent transport coefficients. In the case when the viscosity μ (θ) = θ α and the heat-conductivity κ (θ) = θ β with α , β ∈ 0 , ∞) , we prove the global-in-time existence of strong solutions under some assumptions on the growth exponent α and the initial data. As a byproduct, the nonlinearly exponential stability of the solution is obtained. It is worth pointing out that the initial data could be large if α ≥ 0 is small, and the growth exponent β ≥ 0 can be arbitrarily large. [ABSTRACT FROM AUTHOR]