Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

Details Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations

2007-05-27

arxiv.org/abs/0705.3972v1

Mathematics

Analysis of PDEs

Scientific paper

We investigate the long-term dynamics of the three-dimensional Navier-Stokes-Voight model of viscoelastic incompressible fluid. Specifically, we derive upper bounds for the number of determining modes 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 we consider the Navier-Stokes-Voight model as a non-viscous (inviscid) regularization of the three-dimensional Navier-Stokes equations. Furthermore, we also show 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 $\nu \to 0$.

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