导热且发生化学反应混合物的定常可压缩流体模型的存在性分析
Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures
AI总结：
本文研究导热、化学反应可压缩混合物的定常 Navier-Stokes-Fourier 系统，利用熵与能量平衡、压力估计及紧性技术，证明了含交叉扩散等一般效应的大数据弱解存在性。
摘要：
本文证明了用于发生化学反应流体混合物的定常可压缩 Navier-Stokes-Fourier 系统存在大数据弱解。文中考虑满足若干结构性假设的一般自由能，其压力包含 $\gamma$ 次幂律。该模型在热力学上是一致的，并且将 Fick-Onsager 形式的 Maxwell-Stefan 交叉扩散方程作为特例包含在内。与以往工作相比，本文分析了一个非常一般的模型类别，包括交叉扩散效应、温度梯度、可压缩流体以及不同摩尔质量。先验估计由熵平衡和总能量平衡导出。总质量密度的紧性来自压力在 $L^p$（其中 $p>1$）中的估计、有效粘性通量恒等式，以及与 Feireisl 振荡亏测度相关的一致界。这些界在很大程度上依赖于自由能的凸性和相对化学势的强收敛性。
英文摘要：
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.
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。
