We show existence of global weak solutions of the Rosensweig model of ferrofluids, using DiPerna-Lions’ theory of compressible fluids. Then, we investigate the relaxation to equilibrium ϵ→0 using the relative entropy method. If the limiting system has a Lipschitz continuous solution, we can show a convergence rate in ϵ, if the limiting system has only a weak solution, we obtain strong convergence of a subsequence in L^2.