Global existence and asymptotic analysis of weak solutions to the equations of Ferrohydrodynamics

In this paper, we consider the three-dimensional equations of Ferrohydrodynamics describing the motion of an incompressible ferrofluid under the action of an external magnetic field. We first consider the system introduced by Rosensweig. We establish the existence of globally defined finite energy weak solutions and also investigate the large-time behavior of such solutions. Then we study the asymptotic behavior of the solutions as some physical parameters in the angular momentum equations tend to zero, we prove that the limit functions will be weak solutions of the equations proposed by Shliomis. This shows rigorously the exact relationship of these two principal systems which describe the motion of ferrofluids.