HOMOGENIZATION OF TRAJECTORY STATISTICAL SOLUTIONS FOR THE 3D INCOMPRESSIBLE MAGNETO-MICROPOLAR FLUIDS

This article investigates the 3D incompressible magneto-micropolar fluids containing rapidly oscillating external force and angular momentum with respect to spatial variables. Under suitable assumptions on the oscillating external force and angular momentum, the existence of the trajectory attractor A(epsilon)(tr) and trajectory statistical solution mu(epsilon,w epsilon) is established, as well as the convergence of A(epsilon)(tr) to the trajectory attractor A(0)(tr) of the homogenized fluids. Then we prove the homogenization of trajectory statistical solution by establishing that mu(epsilon,w epsilon) converges to the trajectory statistical solution mu(0,w) of the homogenized fluids as epsilon -> 0(+). Our results reveal that the trajectory statistical information obtained from the 3D incompressible magneto-micropolar fluids with rapidly oscillating external force and angular momentum has certain homogenization effect with respect to spatial variables.