Pullback attractor for non-homogeneous micropolar fluid flows in non-smooth domains

In this paper, which concerns two-dimensional non-autonomous micropolar fluid flows in a Lipschitz bounded domain with non-homogeneous boundary conditions, the existence of a pullback attractor in HH is shown under the following assumptions: the external forces f(t)∈Lloc2(R,V′) satisfying ∫−∞teσs|f(s)|V′2<∞ for some σ>0σ>0 characterized later; and the non-homogeneous boundary condition φ(x)∈L∞(∂Ω)φ(x)∈L∞(∂Ω).