Global attractors and determining modes for the 3D Navier-Stokes-Voight equations Academic Article uri icon

abstract

  • The authors investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, upper bounds for the number of determining modes are derived for the 3D Navier-Stokes-Voight equations and for the dimension of a global attractor of a semigroup generated by these equations. Viewed from the numerical analysis point of view the authors consider the Navier-Stokes-Voight model as a non-viscous (inviscid) regularization of the three-dimensional Navier-Stokes equations. Furthermore, it is also shown that the weak solutions of the Navier-Stokes-Voight equations converge, in the appropriate norm, to the weak solutions of the inviscid simplified Bardina model, as the viscosity coefficient ν → 0. © Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2009.

author list (cited authors)

  • Kalantarov, V. K., & Titi, E. S.

citation count

  • 79

publication date

  • September 2009