多变过程
数学
指数
压缩性
数学分析
粘度
初值问题
指数稳定性
边值问题
指数函数
热力学
非线性系统
指数增长
理论(学习稳定性)
机械
物理
机器学习
量子力学
哲学
计算机科学
语言学
作者
Ying Sun,Jianwen Zhang,Xiaokui Zhao
标识
DOI:10.1016/j.jde.2021.03.044
摘要
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)=θα and the heat-conductivity κ(θ)=θβ 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.
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