论文标题
非定位与无与伦比密度的两相流量的局部扩散界面模型的收敛
Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities
论文作者
论文摘要
我们证明，具有不同密度的不可压缩流体的两相流量具有不同的密度，具有非局部Cahn-Hilliard方程与具有标准“局部” cahn-Hilliard方程的相应系统的弱解。分析是在具有足够平滑的有界结构域的情况下进行的，具有无滑动边界条件的速度和Cahn-Hilliard方程的Neumann边界条件。该证明基于在单个Cahn-Hilliard方程和紧凑性参数中使用的相应结果，用于证明扩散接口模型的弱解决方案。
We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the corresponding system with a standard "local" Cahn-Hilliard equation. The analysis is done in the case of a sufficiently smooth bounded domain with no-slip boundary condition for the velocity and Neumann boundary conditions for the Cahn-Hilliard equation. The proof is based on the corresponding result in the case of a single Cahn-Hilliard equation and compactness arguments used in the proof of existence of weak solutions for the diffuse interface model.
