Averaging of a 3D Navier–Stokes–Voight equation with singularly oscillating forces

For ρ∈[0,1)ρ∈[0,1) and ε∈(0,1)ε∈(0,1), we investigate the uniform attractors of a 3D non-autonomous Navier–Stokes–Voight equation with singularly oscillating forces ut−ν△u−α2△ut+(u⋅∇)u+∇p=f0(t,x)+ε−ρf1(t/ε,x),x∈Ω,∇⋅u=0,x∈Ω,u(t,x)|∂Ω=0,u(τ,x)=uτ(x),τ∈R, together with the averaged equations (corresponding to the limiting case ε=0ε=0) ut−ν△u−α2△ut+(u⋅∇)u+∇p=f0(t,x),x∈Ω,∇⋅u=0,x∈Ω,u(t,x)|∂Ω=0,u(τ,x)=uτ(x),τ∈R. Under suitable assumptions on the external forces, we obtain the uniform boundedness of the related uniform attractor AεAε of the first system, and the convergence of AεAε to the attractor A0A0 of the second system as ε→0+ε→0+.