Determining modes for the 3D Navier-Stokes equations

Abstract

We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blows up, its time average is uniformly bounded for all solutions on the global attractor. The bound is compared to Kolmogorov's dissipation wavenumber and the Grashof constant.

19 pages

References in corpus (1)

• Determining modes for the surface Quasi-Geostrophic equation

Cited by in corpus (8)

• Determining modes for the surface Quasi-Geostrophic equation
• Regularity criteria for the 3D Navier-Stokes and MHD equations
• On the determining wavenumber for the nonautonomous subcritical SQG equation
• Kolmogorov's dissipation number and determining wavenumber for dyadic models
• Regularity Criterion for the Three-dimensional Boussinesq Equations
• Determining wavenumbers for the incompressible Hall-magneto-hydrodynamics
• Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
• Phenomenologies of intermittent Hall MHD turbulence