H1H1-Uniform attractor and asymptotic smoothing effect of solutions for a nonautonomous micropolar fluid flow in 2D unbounded domains

This paper discusses the long time behavior of solutions for a two-dimensional (2D) nonautonomous micropolar fluid flow in 2D unbounded domains in which the Poincaré inequality holds. We use the energy method to obtain the so-called asymptotic compactness of the family of processes associated with the fluid flow and establish the existence of H1H1-uniform attractor. Then we prove that an L2L2-uniform attractor belongs to the H1H1-uniform attractor, which implies the asymptotic smoothing effect for the fluid flow in the sense that the solutions become eventually more regular than the initial data.