Optimal control of 3D Navier-Stokes-Voigt equations for convex control constraints

We study a distributed optimal control problem for Navier-Stokes-Voigt equations in three-dimensional bounded domains with convex control constraints and a general cost functional. We prove the existence of optimal solutions, the first-order necessary optimality conditions, and the second-order sufficient optimality conditions as well as the Lipschitz stability of optimal solutions with respect to the initial data.