Global strong solutions to the Shliomis system for ferrofluids in a bounded domain
Chuangen Xie · Mathematical Methods in the Applied Sciences · 2019
We consider the partial differential equations proposed by Shliomis to model the dynamics of an incompressible viscous ferrofluid submitted to an external magnetic field. The Shliomis system consists of the incompressible Navier‐Stokes equations, the magnetization equations, and the magnetostatic equations. The magnetization equations is of Bloch type, and no regularizing term is added. We prove the global existence of unique strong solution to the initial boundary value problem for the system in a bounded domain, with the small initial data and external magnetic field but without any restrictions on the physical parameters. The novelty of the analysis is to introduce a linear combination of magnetic fields.