Decay characterization of the solutions to the Navier–Stokes–Voigt equations with damping

Abstract

The Navier–Stokes–Voigt equations are a regularization of the Navier–Stokes equations. Sharing some asymptotic and statistical properties, they have been used in direct numerical simulations of the latter. In this article, we characterize the decay rate of the solutions to the Navier–Stokes–Voigt equations with damping. Applying the Fourier splitting method, we prove the H1 decay of weak solutions for α > 0, β > 2, and μ > ν2.