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

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.