We consider a three-dimensional Navier-Stokes-Voigt equations with memory in lacking instantaneous kinematic viscosity, in presence of Ekman type damping and singularly oscillating external forces depending on a positive parameter $ \varepsilon $. Under suitable assumptions on the memory term and on the external forces, we prove the existence and the uniform (w.r.t. $ \varepsilon $) boundedness as well as the convergence as $ \varepsilon $ tends to $ 0 $ of uniform attractors $ \mathcal A ^\varepsilon $ of a family of processes associated to the model.

中文翻译：

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具有记忆并且奇异振荡的外力的3D Navier-Stokes-Voigt方程的均匀吸引子

我们考虑具有记忆力的三维Navier-Stokes-Voigt方程，该方程缺乏瞬时运动粘度，存在Ekman型阻尼并且根据正参数$ \ varepsilon $奇异地振荡外力。在关于记忆项和外力的适当假设下，我们证明了存在性和均匀性（wrt $ \ varepsilon $）有界以及收敛性，因为$ \ varepsilon $趋向于$ 0 $统一吸引子$ \ mathcal A与模型相关的一系列过程的^ \ varepsilon $。