Weak solutions for a diffuse interface model for two‐phase flows of incompressible fluids with different densities and nonlocal free energies
Weak solutions for a diffuse interface model for two‐phase flows of incompressible fluids with different densities and nonlocal free energies
复制标题
不同密度和非局域自由能不可压缩流体两相流扩散界面模型的弱解
DOI：
10.1002/mma.6111
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发表时间：
2020
影响因子：
2.9
通讯作者：
Yutaka Terasawa
中科院分区：
文献类型：
--
作者：
Helmut Abels;Yutaka Terasawa
我们考虑了两种不同密度的粘性不可压缩牛顿流体在二维和三维空间有界域中流动的扩散界面模型，并证明了其弱解的存在。与早期的贡献相比，我们研究了具有奇异非局域自由能的模型，该模型控制体积分数的 Hα/2-范数。我们借助隐式时间离散化证明了大时间弱解的存在。
We consider a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions and prove existence of weak solutions for it. In contrast to earlier contributions, we study a model with a singular nonlocal free energy, which controls theHα/2‐norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.