Amirat, Youcef; Hamdache, Kamel; Murat, François Global weak solutions to equations of motion for magnetic fluids. (English) Zbl 1162.76408 J. Math. Fluid Mech. 10, No. 3, 326-351 (2008). Summary: We study the differential system governing the flow of an incompressible ferrofluid under the action of a magnetic field. The system consists of the Navier-Stokes equations, the angular momentum equation, the magnetization equation, and the magnetostatic equations. We prove, by using the Galerkin method, a global in time existence of weak solutions with finite energy of an initial boundary-value problem and establish the long-time behavior of such solutions. The main difficulty is due to the singularity of the gradient magnetic force. Cited in 23 Documents MSC: 76W05 Magnetohydrodynamics and electrohydrodynamics 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 35Q30 Navier-Stokes equations 35Q35 PDEs in connection with fluid mechanics Keywords:magnetic fluid flow; Navier-Stokes equations; magnetization; angular momentum; weak solutions PDFBibTeX XMLCite \textit{Y. Amirat} et al., J. Math. Fluid Mech. 10, No. 3, 326--351 (2008; Zbl 1162.76408) Full Text: DOI