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

2021/05/10 by Martin Kalousek, Kalousek, Martin, Sourav Mitra +3
Materials Science · Mathematics · #35D30 #35Q35 #76D05 #76T06 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2105.04291

openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Grün 2011.

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