Cauchy problem for the Navier–Stokes equations with temperature-dependent transport coefficients and large data

In this paper, we investigate the Cauchy problem for the one-dimensional compressible Navier–Stokes equations with temperature-dependent transport coefficients and large initial data. Specifically, we consider the case where the viscosity coefficient is characterized by [Formula: see text] and the heat conductivity coefficient is given by [Formula: see text], for [Formula: see text]. Our main result establishes the existence and asymptotic stability of a global strong solution provided that the initial data belongs to the [Formula: see text]-space and [Formula: see text] is sufficiently small. This finding provides a positive response to the question posed in [Remarks 1.3 and 1.4 in T. Wang and H. J. Zhao, One-dimensional compressible heat-conducting gas with temperature-dependent viscosity, Math. Models Methods Appl. Sci. 26 (2016) 2237–2275].