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

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