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arXiv · 1507.01075

Determining modes for the surface Quasi-Geostrophic equation

Alexey Cheskidov·Mimi Dai
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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.

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Alexey Cheskidov, Mimi Dai. 2015-07-04. Determining modes for the surface Quasi-Geostrophic equation. https://doi.org/10.1016/j.physd.2018.03.003

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