Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations Academic Article

abstract

• We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier-Stokes system and Navier-Stokes system with damping. In the first case we obtain the previously known estimates in an explicit form, which are larger than the fractal dimension of the global attractor. However, for the Navier-Stokes system with damping, our estimates for the number of the determining modes and nodes are comparable to the sharp estimates for the fractal dimension of the global attractor. Our investigation of the damped-driven 2-D Navier-Stokes system is inspired by the Stommel-Charney barotropic model of ocean circulation where the damping represents the Rayleigh friction. We remark that our results equally apply to the viscous Stommel-Charney model. 2006 Springer.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF NONLINEAR SCIENCE

author list (cited authors)

• Ilyin, A. A., & Titi, E. S.

citation count

• 34

complete list of authors

• Ilyin, AA||Titi, ES

publication date

• June 2006

publisher

• Springer Nature  Publisher

published in

• Journal of Nonlinear Science  Journal

keywords

• Barotropic Ocean Circulation Model
• Determining Modes And Nodes
• Fractal Dimension
• Navier-stokes Equations
• Stommel-charney Model

Digital Object Identifier (DOI)

• 10.1007/s00332-005-0720-7

start page

• 233

end page

• 253

volume

• 16

issue

• 3

URL

• http://dx.doi.org/10.1007/s00332-005-0720-7

user-defined tag

• 14 Life Below Water