Global weak solutions to a ferrofluid flow model

We are concerned with the global solvability of the differential system introduced by Shliomis to describe the flow of a colloidal suspension of magnetized nanoparticles in a nonconducting liquid, under the action of an external magnetic field. The system is a combination of the Navier-Stokes equations, the magnetization equation, and the magnetostatic equations. We prove, by using a method of regularization, the existence of global-in-time weak solutions with finite energy to an initial boundary-value problem and establish the long-time behaviour of such solutions. The main difficulty is due to the singularity of the gradient magnetic force and the torque.