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Averaging of a 3D Navier-Stokes-Voight equation with singularly oscillating forces. (English) Zbl 1239.35128

Summary: For ρ[0,1) and ε(0,1), we investigate the uniform attractors of a 3D non-autonomous Navier-Stokes-Voight equation with singularly oscillating forces

u t -νΔu-α 2 Δu t +(u·)u+p=f 0 (t,x)+ε -ρ f 1 (t/ε,x),xΩ,·u=0,xΩ,u(t,x)| Ω =0,u(τ,x)=u τ (x),τ,

together with the averaged equations (corresponding to the limiting case ε=0)

u t -νΔu-α 2 Δu t +(u·)u+p=f 0 (t,x),xΩ,·u=0,xΩ,u(t,x)| Ω =0,u(τ,x)=u τ (x),τ·

Under suitable assumptions on the external forces, we obtain the uniform boundedness of the related uniform attractor 𝒜 ε of the first system, and the convergence of 𝒜 ε to the attractor 𝒜 ε of the second system as ε0 + .

35Q35PDEs in connection with fluid mechanics
35B41Attractors (PDE)
76D05Navier-Stokes equations (fluid dynamics)
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