Suitable weak solutions to the 3D Navier–Stokes equations are constructed with the Voigt approximation

In this paper we consider the Navier–Stokes equations supplemented with either the Dirichlet or vorticity-based Navier slip boundary conditions. We prove that weak solutions obtained as limits of solutions of the Navier–Stokes–Voigt model satisfy the local energy inequality, and we also prove certain regularity results for the pressure. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions through a Fourier–Galerkin finite-dimensional approximation in the space variables.