Professor Otelbaev of Kazahkstan claims to have proved the existence of solutions to the Navier-Stokes equations (with viscosity non-zero) in the periodic boundary condition case, cf.: (and has a 100 page article/preprint in Russian).

Suppose under some general initial conditions the Navier-Stokes equations have a solution for all time. (such as in in the "no breakdown" scenarios in the Navier-Stokes Clay Problem).

Is the thinking that this could still adequately approximate "turbulent flow" ? Or maybe the thinking is "undecided" ?