Exponential approximations for the primitive equations of the ocean

Roger Temam; D. Wirosoetisno

doi:10.3934/dcdsb.2007.7.425

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2007, Volume 7, Issue 2: 425-440. Doi: 10.3934/dcdsb.2007.7.425

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Exponential approximations for the primitive equations of the ocean

Roger Temam^1, and
D. Wirosoetisno^2,

1.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405
2.
Department of Mathematical Sciences, University of Durham, Durham DH1 3LE

Received: August 31, 2006

Revised: October 31, 2006

Published: August 2007

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Abstract

We show that in the limit of small Rossby number $\varepsilon$, the primitive equations of the ocean (OPEs) can be approximated by "higher-order quasi-geostrophic equations'' up to an exponential accuracy in $\varepsilon$. This approximation assumes well-prepared initial data and is valid for a timescale of order one (independent of $\varepsilon$). Our construction uses Gevrey regularity of the OPEs and a classical method to bound errors in higher-order perturbation theory.

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Mathematics Subject Classification: Primary: 35B25, 76U05.

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