On convergence of trajectory attractors of the 3D Navier-Stokes-α model as α approaches 0
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We study the relations between the long-time dynamics of the Navier-Stokes-α model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes-α model converge to the trajectory attractor U0 of the 3D Navier-Stokes system as the time approaches infinity and α approaches zero. In particular, we show that the trajectory attractor Uα of the Navier-Stokes-α model converges to the trajectory attractor U0 of the 3D Navier-Stokes system α → 0+. We also construct the minimal limit U min(⊆U0) of the trajectory attractor U α as α → 0+ and prove that the set Umin is connected and strictly invariant. © 2007 RAS(DoM) and LMS.
author list (cited authors)
Vishik, M. I., Titi, E. S., & Chepyzhov, V. V.