发表机构
Nanchang University（南昌大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该文研究一维全可压缩Navier-Stokes方程，在粘性指数和波强度足够小、初始扰动可大的条件下，证明了粘性接触波与稀疏波叠加的全局稳定性，并给出比容和温度的一致上下界。
AI 中文摘要
我们研究一维全可压缩Navier-Stokes方程的Cauchy问题，其中粘性系数为$\mu(\theta)=\tilde\mu\theta^\alpha$，热传导系数为$\kappa(\theta)=\tilde\kappa\theta^\beta$。对于每个固定的$\beta\ge0$，我们证明，在粘性指数$\alpha$和总波强度足够小的条件下，粘性接触波与稀疏波组合的全局稳定性。初始扰动在$H^1$中可以是大的，并且假设比容和温度具有正的初始下界。解相对于波在$H^1$中保持一致有界，并且当时间趋于无穷时一致收敛于该波。我们证明比容和温度都具有时间一致的下界和上界。对对数体积导数和温度梯度的估计随后封闭了$H^1$估计，而不需要初始比容的二阶导数。
英文摘要
We study the Cauchy problem for the one-dimensional full compressible Navier--Stokes equations with viscosity $μ(θ)=\tildeμθ^α$ and heat conductivity $κ(θ)=\tildeκθ^β$. For each fixed $β\ge0$, we prove the global stability of the combination of a viscous contact wave with rarefaction waves, provided that the viscosity exponent $α$ and the total wave strength are sufficiently small. The initial perturbation may be large in $H^1$, and the specific volume and temperature are assumed to have positive initial lower bounds. The solution remains uniformly bounded in $H^1$ relative to the wave, and converges uniformly to that wave as time tends to infinity. We show that both the specific volume and the temperature admit time-uniform lower and upper bound. Estimates for the logarithmic volume derivative and the temperature gradient then close the $H^1$ estimates without requiring a second derivative of the initial specific volume.
