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Global attractors and determining modes for the 3D Navier-Stokes-Voight equations. (English) Zbl 1178.37112
Summary: 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 $\nu \to 0$.
##### MSC:
 37L30 Attractors and their dimensions, Lyapunov exponents 35Q35 PDEs in connection with fluid mechanics 35Q30 Stokes and Navier-Stokes equations 35B40 Asymptotic behavior of solutions of PDE
##### References:
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