On the convergence of solutions of the Leray-$alpha $ model to the trajectory attractor of the 3D Navier-Stokes system Academic Article uri icon

abstract

  • We study the relations between the global dynamics of the 3D Leray-α model and the 3D Navier-Stokes system. We prove that time shifts of bounded sets of solutions of the Leray-α model converges to the trajectory attractor of the 3D Navier-Stokes system as time tends to infinity and a approaches zero. In particular, we show that the trajectory attractor of the Leray-a model converges to the trajectory attractor of the 3D Navier-Stokes system when α → 0+.

author list (cited authors)

  • V. Chepyzhov, V., S. Titi, E., & I. Vishik, M.

citation count

  • 40

publication date

  • January 2007