Homogenization of a NonLinear Strongly Coupled Model of Magnetorheological Fluids

This paper concerns the rigorous periodic homogenization for a nonlinear strongly coupled system, which models suspension of magnetizable rigid particles in nonconducting carrier viscous Newtonian fluid. The fluid drags and thus alters magnetic field. Vice versa, field acts on particles, turn affect via no-slip boundary condition. As size approaches zero, it is shown that suspension’s behavior governed by generalized magnetohydrodynamic where modeled stationary Navier–Stokes while Maxwell equations. A corrector result from theory two-scale convergence allows us to obtain limit product several weakly convergent sequences, div-curl lemma, typical tool these types problems, not applicable.