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

0572855 - MÚ 2024 RIV DE eng J - Journal Article
Kalousek, Martin - Mitra, Sourav - Schlömerkemper, A.
Existence of weak solutions to a diffuse interface model involving magnetic fluids with unmatched densities.
Nodea-Nonlinear Differential Equations and Applications. Roč. 30, č. 4 (2023), č. článku 52. ISSN 1021-9722. E-ISSN 1420-9004
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : Cahn-Hilliard equations * diffuse interface model * global existence * implicit time discretization
OECD category: Pure mathematics
Impact factor: 1.2, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00030-023-00852-0

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 et al. (Models Methods Appl Sci 22(3):1150013, 2011).
Permanent Link: https://hdl.handle.net/11104/0343421