Existence and homogenization of trajectory statistical solutions for the 3D incompressible Hall-MHD equations

In this article, the authors first investigated the 3D incompressible Hall-magnetohydrodynamic (Hall-MHD) equations, they proved the existence of the trajectory attractor, and used this trajectory attractor and generalized Banach limit to construct the trajectory statistical solutions of equations. Then, they studied the 3D incompressible Hall-MHD equations containing rapidly oscillating external force with respect to spatial variables. Under suitable assumptions on the oscillating external force, they verified the homogenization of trajectory statistical solutions by establishing that the trajectory statistical solutions of the oscillating equations converged to the trajectory statistical solutions of the homogenized equations.