×

Global weak solutions to equations of motion for magnetic fluids. (English) Zbl 1162.76408

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.

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
PDFBibTeX XMLCite
Full Text: DOI