Strong solutions to the equations of a ferrofluid flow model

We study the differential system introduced by M.I. Shliomis to describe the motion of a ferrofluid driven by an external magnetic field. The system is a combination of the Navier–Stokes equations, the magnetization equation and the magnetostatic equations. No regularizing term is added to the magnetization equation. We prove the local-in-time existence of strong solutions to the system.