SIAM Journal on Mathematical Analysis, Volume 52, Issue 2, Page 2179-2197, January 2020.
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is defined by a state equation imposed by the volume extension of the mixture. These model assumptions lead to a parabolic-hyperbolic system for the mass densities. The global-in-time existence of classical and weak solutions is proved in a bounded domain with no-penetration boundary conditions. The idea is to decompose the system into a porous-medium-type equation for the volume extension and transport equations for the modified number fractions. The existence proof is based on parabolic regularity theory, the theory of renormalized solutions, and an approximation of the velocity field.

中文翻译：

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压力梯度驱动的流体混合物的交叉扩散系统分析

SIAM数学分析杂志，第52卷，第2期，第2179-2197页，2020年1月。
考虑了服从质量连续性方程的多组分等温可压缩流体中的对流输运。根据达西定律，速度与负压梯度成比例，并且压力由混合物体积扩展所施加的状态方程式定义。这些模型假设导致质量密度为抛物线-双曲线系统。在无穿透边界条件的有界域中证明了经典解和弱解的全局时间存在性。想法是将系统分解为用于体积扩展的多孔介质类型方程式和用于修改的数量分数的传输方程式。存在性证明基于抛物线正则性理论，重归一化理论和速度场的近似。