A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations consist of the stationary Navier–Stokes equations for compressible fluids and a stationary Cahn–Hilliard type equation for the mass concentration difference. Approximate solutions are constructed through a two-level approximation procedure, and the limit of the sequence of approximate solutions is obtained by a weak convergence method. New ideas and estimates are developed to establish the existence of weak solutions with a wide range of adiabatic exponent.

中文翻译：

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可压缩流扩散界面模型的固定 Cahn-Hilliard-Navier-Stokes 方程

考虑了扩散界面模型的偏微分方程系统，用于在三维有界域中两种宏观不混溶的粘性牛顿流体的静止运动。控制方程包括可压缩流体的固定 Navier-Stokes 方程和质量浓度差的固定 Cahn-Hilliard 型方程。通过两级逼近过程构造逼近解，通过弱收敛方法得到逼近解序列的极限。开发了新的想法和估计来确定具有广泛绝热指数的弱解的存在。