We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick–Onsager or Maxwell–Stefan closure approach. Mechanical forces result into one single convective mixture velocity, the barycentric one, which obeys the Navier–Stokes equations. The thermodynamic pressure is defined by the Gibbs–Duhem equation. Chemical potentials and pressure are derived from a thermodynamic potential, the Helmholtz free energy, with a bulk density allowed to be a general convex function of the mass densities of the constituents.

The resulting PDEs are of mixed parabolic–hyperbolic type. We prove two theoretical results concerning the well-posedness of the model in classes of strong solutions: 1. The solution always exists and is unique for short-times and 2. If the initial data are sufficiently near to an equilibrium solution, the well-posedness is valid on arbitrary large, but finite time intervals. Both results rely on a contraction principle valid for systems of mixed type that behave like the compressible Navier–Stokes equations. The linearised parabolic part of the operator possesses the self map property with respect to some closed ball in the state space, while being contractive in a lower order norm only. In this paper, we implement these ideas by means of precise a priori estimates in spaces of exact regularity.

我们考虑一个偏微分方程系统，该系统描述了多组分等温可压缩流体中的质量传递。扩散通量遵循Fick-Onsager或Maxwell-Stefan封闭法。机械力导致一个单一的对流混合速度，即重心速度，服从Navier–Stokes方程。热力学压力由Gibbs-Duhem方程定义。化学势和压力来自热力学势，即亥姆霍兹自由能，其堆积密度被允许作为组分质量密度的一般凸函数。

生成的PDE属于混合抛物线-双曲线型。我们证明了关于模型在强解类别中的适定性的两个理论结果：1.该解始终存在，并且对于短时间而言是唯一的；以及2.如果初始数据足够接近平衡解，则该阱-姿势性在任意大但有限的时间间隔内有效。这两个结果都依赖于收缩原理，该原理对于混合类型的系统有效，该混合系统的行为类似于可压缩的Navier–Stokes方程。算子的线性抛物线部分相对于状态空间中的某个闭合球具有自映射特性，而仅在较低阶范数中收缩。在本文中，我们通过精确的先验来实现这些想法 精确规律性空间中的估计。