This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier–Stokes equations coupled with an evolutionary equation for the magnetization vector and the Cahn–Hilliard equations. We show global in time existence of weak solutions to the system using the time discretization method.

中文翻译：

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磁流体扩散界面模型的弱解的整体存在

本文致力于对两种牛顿不可压缩磁性流体的扩散界面流进行建模的偏微分方程系统的推导和分析。该系统由不可压缩的Navier-Stokes方程以及磁化矢量的演化方程和Cahn-Hilliard方程组成。我们使用时间离散方法显示了系统的弱解在时间上的整体存在性。