Determining modes for the surface Quasi-Geostrophic equation
arXiv:1507.01075 · doi:10.1016/j.physd.2018.03.003
Abstract
We introduce a determining wavenumber for the surface quasi-geostrophic (SQG) equation defined for each individual trajectory and then study its dependence on the force. While in the subcritical and critical cases this wavenumber has a uniform upper bound, it may blow up when the equation is supercritical. A bound on the determining wavenumber provides determining modes, which in some sense measure the number of degrees of freedom of the flow, or resolution needed to describe a solution to the SQG equation.
25 pages
References in corpus (5)
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Cited by in corpus (9)
- Determining modes for the 3D Navier-Stokes equations
- Regularity criteria for the 3D Navier-Stokes and MHD equations
- On the determining wavenumber for the nonautonomous subcritical SQG equation
- Low modes regularity criterion for a chemotaxis-Navier-Stokes system
- Regularity Criterion for the Three-dimensional Boussinesq Equations
- Kolmogorov's dissipation number and the number of degrees of freedom for the 3D Navier-Stokes equations
- Uniqueness and stability of steady-state solution with finite energy to the fractal Burgers equation
- A determining form for the subcritical surface quasi-geostrophic equation
- The barotropic quasi-geostrophic equation under a free surface