Decay of Fourier modes of solutions to the dissipative surface quasi-geostrophic equations on a finite domain

Nikolai Chernov and Dong Li

Chaos, Solitons & Fractals, 2012, vol. 45, issue 9, 1192-1200

Abstract: We consider the two dimensional dissipative surface quasi-geostrophic equation on the unit square with mixed boundary conditions. Under some suitable assumptions on the initial stream function, we obtain existence and uniqueness of solutions in the form of a fast converging trigonometric series. We prove that the Fourier coefficients of solutions have a non-uniform decay: in one direction the decay is exponential and along the other direction it is only power like. We establish global wellposedness for arbitrary large initial data.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:45:y:2012:i:9:p:1192-1200

DOI: 10.1016/j.chaos.2012.06.002

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