In this talk we address the question of whether there exist constant-energy solutions to the 3-D incompressible Navier-Stokes that nevertheless evolve in time. In previous work we constructed such solutions to the simpler (linear) 2-D incompressible Stokes equations. We modify our previous work to construct such solutions in the case of the 3-D incompressible Navier Stokes equations on the torus. In this talk we will review previous results and present their expansion to the case of interest. This is joint work with Radu Dascaliuc.