涉及密度不匹配磁流体的扩散界面模型弱解的存在性
偏微分方程分析
2021-06-09 v2 数学物理
math.MP
摘要
本文中，我们证明了在有界区域（二维与三维）中涉及密度不匹配不可压缩磁流体的扩散界面模型的全局弱解存在性。该模型耦合了不可压缩 Navier-Stokes 方程、磁化矢量的梯度流以及描述两种流体部分混合的 Cahn-Hilliard 动力学。混合物的密度依赖于序参数，且建模（具体而言密度依赖性）受 Abels、Garcke 与 Grün 2011 的启发。
引用
@article{arxiv.2105.04291,
title = {Existence of weak solutions to a diffuse interface model involving magnetic fluids with unmatched densities},
author = {Martin Kalousek and Sourav Mitra and Anja Schlömerkemper},
journal= {arXiv preprint arXiv:2105.04291},
year = {2021}
}
备注
Compared to the earlier version, new references concerning the celebrated Abels, Garcke and Gr\"{u}n model are added and some typos are fixed