AI 中文总结
本文研究一维可压缩Navier-Stokes系统外部压力问题的全局强解，在温度依赖输运系数下，证明大初始数据解的存在性，并分析正压与零压极限下解分别收敛到稳态和膨胀态的代数速率。
AI 中文摘要
我们研究一维粘性、热传导理想多方气体的外部压力问题的全局强解及其大时间行为。粘度和热导率满足$\mu=\tilde\mu\theta^\alpha$和$\kappa=\tilde\kappa\theta^\beta$。对于每个给定的非负压力和每个固定的$\beta\geq0$，只要$\alpha\geq0$足够小，我们允许具有正比容和正温度的大的$H^1$初始数据。当极限外部压力为正时，解具有一致界并收敛到稳态。当极限外部压力为零且所陈述的加权压力条件成立时，归一化解以物理时间中的代数速率收敛到膨胀状态。
英文摘要
We study global strong solutions and their large-time behavior for the one-dimensional outer pressure problem of a viscous, heat-conducting ideal polytropic gas. The viscosity and heat conductivity satisfy $μ=\tildeμθ^α$ and $κ=\tildeκθ^β$. For each prescribed nonnegative pressure and each fixed $β\geq0$, we allow large $H^1$ initial data with positive specific volume and temperature, provided that $α\geq0$ is sufficiently small. When the limiting outer pressure is positive, the solution has uniform bounds and converges to a stationary state. When the limiting outer pressure is zero and the stated weighted pressure conditions hold, the normalized solution converges to an expanding state at an algebraic rate in physical time.
