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 $\mu (\theta )={\theta }^{\alpha }$ and the heat-conductivity $\kappa (\theta )={\theta }^{\beta }$ with $\alpha ,\beta \in [0,\infty )$, 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 $\alpha \ge 0$ is small, and the growth exponent $\beta \ge 0$ can be arbitrarily large.

中文翻译：

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具有依赖于温度的传输系数的可压缩Navier-Stokes方程的非线性指数稳定性

本文涉及一维粘性和导热性与温度有关的理想多相流体的可压缩Navier-Stokes方程的初值和边值问题。在粘度的情况下$\mu （\theta ）={\theta }^{\alpha }$ 和热导率 $\kappa （\theta ）={\theta }^{\beta }$ 和 $\alpha ，\beta \in [0，\infty ）$，我们在增长指数α和初始数据的某些假设下证明了强解在全局时间上的存在。作为副产品，获得了溶液的非线性指数稳定性。值得指出的是，如果$\alpha \ge 0$ 小，增长指数 $\beta \ge 0$ 可以任意大。