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