Homogenization of Trajectory Statistical Solutions for the 3D Incompressible Micropolar Fluids with Rapidly Oscillating Terms

Abstract

This article studies the 3D incompressible micropolar fluids with rapidly oscillating terms. The authors prove that the trajectory statistical solutions of the oscillating fluids converge to that of the homogenized fluids provided that the oscillating external force and angular momentum possess some weak homogenization. The results obtained indicate that the trajectory statistical information of the 3D incompressible micropolar fluids has a certain homogenization effect with respect to spatial variables. In addition, our approach is also valid for a broad class of evolutionary equations displaying the property of global existence of weak solutions without a known result of global uniqueness, including some model hydrodynamic equations, MHD equations and non-Newtonian fluids equations.

Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

“…They proved the solutions' decay in L 2 as (1 + t) −1/2 based on a complex diagonalization process to eliminate the linear terms. One may also refer to some important progress in this direction (see [17][18][19][20][21][22][23][24][25] and references therein).…”