LAUSR

Abstract 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.