On the convergence of solutions of the Leray-\(\alpha\) model to the trajectory attractor of the 3D Navier-Stokes system (Q2372656)

The authors study the connection between the long-time dynamics of the Leray-\(\alpha\) model and the 3D Navier-Stokes equations as \(\alpha \rightarrow 0+\). It is shown that time shifts of bounded sets of solutions of the Leray-\(\alpha\) model (in particular the trajectories attractor) converge to the trajectory attractor of the 3D Navier-Stokes system as time tends to infinity and \(\alpha\) approaches zero.