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arXiv · 0705.3972

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

Varga K. Kalantarov·Edriss S. Titi
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Abstract

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 $ν\to 0$.

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Varga K. Kalantarov, Edriss S. Titi. 2007-05-27. Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations. https://arxiv.org/abs/0705.3972

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