Three‐dimensional Navier‐Stokes‐Voight equation with a memory and the Brinkman‐Forchheimer damping term

In this paper, we consider the 3D Navier‐Stokes‐Voight model with a nonlinear damping, where the instantaneous kinematic viscosity is replaced by a memory through a distributed delay effect. We prove that the system possesses global and exponential attractors A ε , where ε ∈(0,1) is the scaling parameter in the memory kernel. We also prove that the model converges to the classical Navier‐Stokes‐Voight model with nonlinear damping when ε →0 as t → ∞ . Our results have extended those in Plinio et al.