一维粘性可压缩热传导介质非单调状态方程的稳定性
Stabilization for equations of one-dimensional viscous compressible heat-conducting media with nonmonotone equation of state
摘要：
我们考虑描述粘性可压缩热传导和“自引力”介质运动的Navier-Stokes系统。我们使用相对于温度$θ$线性的形式$p(η,θ)=p_0(η)+p_1(η)θ$的状态函数，但我们承认$η$的相当一般的非单调函数$p_0$和$p_1$，这使我们能够处理核流体（其中$p$和$η$是压力和比容）或热粘弹固体的各种物理模型。对于一个相关的初边值问题与“固定自由”的边界条件和可能的大数据，我们证明了一个集合的估计独立于时间间隔的解决方案，包括双边界限$η$，连同其渐近行为$t\to \infty$。也就是说，我们建立了点态稳定性，并在$L^q$中为$η$，在$L^2$中为$θ$，在$L^q$中为$v$（速度），对任何$q\in[2,\infty)$。
英文摘要：
We consider the Navier-Stokes system describing motions of viscous compressible heat-conducting and "self-gravitating" media. We use the state function of the form $p(η,θ)=p_0(η)+p_1(η)θ$ linear with respect to the temperature $θ$, but we admit rather general nonmonotone functions $p_0$ and $p_1$ of $η$, which allows us to treat various physical models of nuclear fluids (for which $p$ and $η$ are the pressure and specific volume) or thermoviscoelastic solids. For an associated initial-boundary value problem with "fixed-free" boundary conditions and possibly large data, we prove a collection of estimates independent of time interval for solutions, including two-sided bounds for $η$, together with its asymptotic behaviour as $t\to \infty$. Namely, we establish the stabilization pointwise and in $L^q$ for $η$, in $L^2$ for $θ$, and in $L^q$ for $v$ (the velocity), for any $q\in[2,\infty)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
