English

Existence of weak solutions to a diffuse interface model involving magnetic fluids with unmatched densities

Analysis of PDEs 2021-06-09 v2 Mathematical Physics math.MP

Abstract

In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible Navier-Stokes equations, gradient flow of the magnetization vector and the Cahn-Hilliard dynamics describing the partial mixing of two fluids. The density of the mixture depends on an order parameter and the modelling, specifically the density dependence, is inspired from Abels, Garcke and Gr\"{u}n 2011.

Keywords

Cite

@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}
}

Comments

Compared to the earlier version, new references concerning the celebrated Abels, Garcke and Gr\"{u}n model are added and some typos are fixed