  This article establishes the global existence of weak solutions to a model
proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics
of ferrofluids. The system is expressed by the conservation of linear momentum,
the incompressibility condition, the conservation of angular momentum, and the
evolution of the magnetization. The existence proof is inspired by the
DiPerna-Lions theory of renormalized solutions. In addition, the rigorous
relaxation limit of the equations of ferrohydrodynamics towards the
quasi-equilibrium is investigated. The proof relies on the relative entropy
method, which involves constructing a suitable functional, analyzing its time
evolution and obtaining convergence results for the sequence of approximating
solutions.
