Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
By Varga K. Kalantarov, Edriss S. Titi. 2007
200 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/13b2624c882bff16425bfe7a8e877bc84e32083b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Control and Systems Engineering
Citations in the corpus
- The stabilized extrapolated trapezoidal finite-element method for the Navier–Stokes equations (2009, methodology): “It is related to the simple Kelvin-Voight model of viscoelasticity, Oskolkov [O80], Kalantarev and Titi [KT07].”