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

Abstract In this article we prove the global existence of weak solutions for a diffuse interface model in bounded domain (both 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The couples Navier–Stokes equations, gradient flow magnetization vector Cahn–Hilliard dynamics describing partial mixing two fluids. density mixture depends on an order parameter modelling (specifically dependence) is inspired from Abels et al. (Models Methods Appl Sci 22(3):1150013, 2011).