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

摘要

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 epsilon, where epsilon is an element of(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 epsilon -> 0 as t ->infinity. Our results have extended those in Plinio et al.