arXiv:1507.01075 Abstract | arXiv Analytics

arXiv:1507.01075 [math.AP]Abstract References Reviews Resources

Determining modes for the surface Quasi-Geostrophic equation

Published 2015-07-04Version 1

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.

Comments: 22 pages

Categories: math.AP

Subjects: 35Q35, 37L30

Keywords: surface quasi-geostrophic equation, determining modes, determining wavenumber, uniform upper bound, sense measure

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