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

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. Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2009.

authors

• Titi, Edriss

published proceedings

• CHINESE ANNALS OF MATHEMATICS SERIES B

author list (cited authors)

• Kalantarov, V. K., & Titi, E. S.

citation count

• 104

complete list of authors

• Kalantarov, Varga K||Titi, Edriss S

publication date

• November 2009

publisher

• Springer Nature  Publisher

keywords

• Determining Modes
• Global Attractor
• Navier-stokes-voight
• Navier-stokes-voigt
• Regularization Of The Navier-stokes
• Turbulence Models
• Viscoelastic Models

Digital Object Identifier (DOI)

• 10.1007/s11401-009-0205-3

start page

• 697

end page

• 714

volume

• 30

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1007%2Fs11401-009-0205-3