On the regularity and convergence of solutions to the 3D Navier–Stokes–Voigt equations

Abstract In this paper we consider the 3D Navier–Stokes–Voigt equations with periodic boundary conditions. We first prove the higher-order global regularity, including both Sobolev and Gevrey regularity, of solutions to the Navier–Stokes–Voigt equations. Then we show the convergence of solutions of the 3D Navier–Stokes–Voigt equations to the corresponding strong solution of the limit 3D Navier–Stokes equations on the interval of existence of the latter as the parameter tends to zero.