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Recently, the Navier-Stokes-Voight (NSV) model of viscoelastic incompressiblefluid has been proposed as a regularization of the 3D Navier-Stokes equationsfor the purpose of direct numerical simulations. In this work we prove that theglobal attractor of the $D NSV equations, driven by an analytic forcing,consists of analytic functions. A consequence of this result is that thespectrum of the solutions of the 3D NSV system, lying on the global attractor,have exponentially decaying tail, despite the fact that the equations behavelike a damped hyperbolic system, rather than the parabolic one. This resultprovides an additional evidence that the 3D NSV with the small regularizationparameter enjoys similar statistical properties as the 3D Navier-Stokesequations. Finally, we calculate a lower bound for the exponential decayingscale -- the scale at which the spectrum of the solution start to decayexponentially, and establish a similar bound for the steady state solutions ofthe 3D NSV and 3D Navier-Stokes equations. Our estimate coincides with similaravailable lower bound for the smallest dissipation length scale of solutions ofthe 3D Navier-Stokes equations.

Gevrey regularity of the global attractor of the 3D Navier-Stokes-Voight equations