On convergence of trajectory attractors of the 3D Navier-Stokes-alpha model as alpha approaches 0 uri icon

abstract

  • We study the relations between the long-time dynamics of the Navier-Stokes- model and the exact 3D Navier-Stokes system. We prove that bounded sets of solutions of the Navier-Stokes- model converge to the trajectory attractor U0 of the 3D Navier-Stokes system as the time approaches infinity and approaches zero. In particular, we show that the trajectory attractor U of the Navier-Stokes- model converges to the trajectory attractor U0 of the 3D Navier-Stokes system 0+. We also construct the minimal limit U min(U0) of the trajectory attractor U as 0+ and prove that the set Umin is connected and strictly invariant. 2007 RAS(DoM) and LMS.

published proceedings

  • SBORNIK MATHEMATICS

author list (cited authors)

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

citation count

  • 22

complete list of authors

  • Vishik, MI||Titi, ES||Chepyzhov, VV

publication date

  • December 2007