Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities
Analysis of PDEs
2022-01-19 v1
Abstract
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.
Cite
@article{arxiv.2201.06101,
title = {Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities},
author = {Helmut Abels and Yutaka Terasawa},
journal= {arXiv preprint arXiv:2201.06101},
year = {2022}
}
Comments
12 pages