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

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  • Chernov, Nikolai
  • Li, Dong

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.

Suggested Citation

  • Chernov, Nikolai & Li, Dong, 2012. "Decay of Fourier modes of solutions to the dissipative surface quasi-geostrophic equations on a finite domain," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1192-1200.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:9:p:1192-1200
    DOI: 10.1016/j.chaos.2012.06.002
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