Stability of compressible Navier–Stokes equations with temperature-dependent transport coefficients

This paper focuses on investigating the initial boundary value problem of compressible Navier–Stokes equations for ideal polytropic fluids that are viscous, heat-conducting, and one-dimensional, with temperature-dependent transport coefficients. Our aim is to establish the global well-posedness of a strong solution with initial data belonging to the \(H^2\times H^1\times H^1\) $H^2\times H^1\times H^1$ -space, and subsequently obtain \(H^2\) $H^2$ -nonlinearly exponential stability of such strong solution.