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| Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations |
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Citation： |
Varga K. KALANTAROV,Edriss S. TITI.Global Attractors and Determining Modes for the 3D Navier-Stokes-Voight Equations[J].Chinese Annals of Mathematics B,2009,30(6):697~714 |
| Page view： 2140
Net amount： 1687 |
Authors： |
Varga K. KALANTAROV; Edriss S. TITI; |
Foundation： |
the Scientific and Research Council of Turkey (No. 106T337), the ISF Grant (No.
120/6), the BSF Grant (No. 2004271), and the National Science Foundation (Nos. DMS-0504619, DMS-
0708832). |
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| 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 ! 0. |
Keywords： |
Navier-Stokes-Voight, Navier-Stokes-Voigt, Global attractor, Determining
modes, Regularization of the Navier-Stokes, Turbulence models, Viscoelastic
models |
Classification： |
37L30, 35Q35, 35Q30, 35B40 |
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