发表机构
Shanghai Jiao Tong University; Zhejiang Sci-Tech University; Shanghai Lixin University of Accounting and Finance（上海交通大学; 浙江理工大学; 上海立信会计金融学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究一维全可压缩Navier-Stokes方程在温度依赖系数和真空下的全局强解存在性，通过初始层权重和对称化分离热模式与动量模式，证明高边界温度下大数据的强解及指数松弛。
AI 中文摘要
我们研究一维全可压缩Navier--Stokes系统的初边值问题，其中粘性和热传导系数分别为$\mu(\theta)=\mu\theta^\alpha$和$\kappa(\theta)=\kappa\theta^\beta$。初始密度非负且允许为零。对于$\alpha>2$和$\beta>2\alpha+4$，我们证明了对于任意大的相容$H^2$数据，只要给定的边界温度相对于其大小足够高，就存在全局强解。当边界温度趋于无穷时，不需要速度或温度扰动缩小。一个移位的初始层权重和两个物质导数方程的精确对称化将快速热模式与动量模式分开。所得估计关于近似中使用的正下界一致，因此能够过渡到真正的真空极限。证明进一步结合了以守恒平均密度为中心的相对熵恒等式、物理有效粘性通量、沿粒子轨迹的Zlotnik型估计以及密度导数的有限时间输运估计。密度保持一致有界，温度保持与给定的边界温度一致可比。在初始层之后，我们建立了真空相容的指数松弛：密度在每个有限$L^p$中收敛到其守恒平均值，速度和温度扰动在$H^1$中衰减，加权物质导数能量以速率$c\bar\theta^{1-\alpha}$衰减。
英文摘要
We study the initial--boundary value problem for the one-dimensional full compressible Navier--Stokes system whose viscosity and heat conductivity are given by $μ(θ)=μθ^α$ and $κ(θ)=κθ^β$, respectively. The initial density is nonnegative and is allowed to vanish. For $α>2$ and $β>2α+4$, we prove the existence of a global strong solution for arbitrarily large compatible $H^2$ data, provided that the prescribed boundary temperature is sufficiently high relative to their size. No velocity or temperature perturbation is required to shrink as the boundary temperature tends to infinity. A shifted initial-layer weight and an exact symmetrization of the two material-derivative equations separate the fast thermal mode from the momentum mode. The resulting estimates are uniform with respect to the positive lower bound used in the approximation and therefore survive the limit to genuine vacuum. The proof further combines a relative-entropy identity centered at the conserved mean density, the physical effective viscous flux, a Zlotnik-type estimate along particle trajectories, and finite-time transport estimates for the density derivatives. The density remains uniformly bounded and the temperature stays uniformly comparable with the prescribed boundary temperature. After the initial layer we establish vacuum-compatible exponential relaxation: the density converges to its conserved mean in every finite $L^p$, the velocity and temperature perturbation decay in $H^1$, and the weighted material-derivative energy decays at rate $c\barθ^{1-α}$.
Comments48 pages
