论文标题
存在用于热传导和化学反应混合物的固定压缩流体模型的存在分析
Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures
论文作者
论文摘要
证明了对化学反应流体混合物的稳定可压缩纳维尔 - 森林系统的大型弱解决方案的存在。一般的自由能被认为满足了一些结构性假设，其中包含$γ$ - 能力定律的压力。该模型在热力学上是一致的，并且包含fick-os-osager形式的麦克斯韦 - 斯坦跨扩散方程，作为一种特殊情况。与以前的工作相比，分析了非常通用的模型类别，包括交叉扩散效应，温度梯度，可压缩流体和不同的摩尔质量。先验估计是从熵平衡和总能量平衡得出的。总质量密度的紧凑性是根据$ l^p $的压力的估计，$ p> 1 $，有效的粘性通量身份以及与Feireisl的振荡缺陷措施相关的均匀界限。这些边界在很大程度上依赖于自由能的凸度和相对化学势的强收敛。
The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure containing a $γ$-power law. The model is thermodynamically consistent and contains the Maxwell-Stefan cross-diffusion equations in the Fick-Onsager form as a special case. Compared to previous works, a very general model class is analyzed, including cross-diffusion effects, temperature gradients, compressible fluids, and different molar masses. A priori estimates are derived from the entropy balance and the total energy balance. The compactness for the total mass density follows from an estimate for the pressure in $L^p$ with $p>1$, the effective viscous flux identity, and uniform bounds related to Feireisl's oscillations defect measure. These bounds rely heavily on the convexity of the free energy and the strong convergence of the relative chemical potentials.
