We consider a Navier-Stokes-Voigt fluid model where the instantaneouskinematic viscosity has been completely replaced by a memory term incorporatinghereditary effects, in presence of Ekman damping. The dissipative character ofour model is weaker than the one where hereditary and instantaneous viscositycoexist, previously studied by Gal and Tachim-Medjo. Nevertheless, we prove theexistence of a regular exponential attractor of finite fractal dimension underrather sharp assumptions on the memory kernel.
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