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The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokesequations that share some of its asymptotic and statistical properties and havebeen used in direct numerical simulations of the latter. In this article wecharacterize the decay rate of solutions to the Navier-Stokes-Voigt equationsin terms of the decay character of the initial datum and study the long timebehaviour of its solutions by comparing them to solutions to the linear part.

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