Decay characterization of solutions to Navier–Stokes–Voigt equations in terms of the initial datum

The Navier–Stokes–Voigt equations are a regularization of the Navier–Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we characterize the decay rate of solutions to the Navier–Stokes–Voigt equations in terms of the decay character of the initial datum and study the long time behavior of its solutions by comparing them to solutions to the linear part.