On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes

Anne C. Bronzi, Ricardo M. S. Rosa

Published 2012-05-24, updated 2013-04-30Version 3

In this paper statistical solutions of the 3D Navier-Stokes-$\alpha$ model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-$\alpha$ model converge to statistical solutions of the exact 3D Navier-Stokes equations as $\alpha$ goes to zero. The statistical solutions considered here arise as families of time-projections of measures in suitable trajectory spaces.