Dh. Chae et C. Foias, ON THE HOMOGENEOUS STATISTICAL SOLUTIONS OF THE 2-D NAVIER-STOKES EQUATIONS, Indiana University mathematics journal, 43(1), 1994, pp. 177-185
We show that the homogeneous statistical solutions of the Navier-Stoke
s equations constructed in [3], satisfy in the two dimensional case bo
th the energy and the enstrophy inequalities.