# American Institute of Mathematical Sciences

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March  2007, 7(2): 425-440. doi: 10.3934/dcdsb.2007.7.425

## Exponential approximations for the primitive equations of the ocean

 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, United Kingdom

Received  September 2006 Revised  November 2006 Published  December 2006

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.
Citation: Roger Temam, D. Wirosoetisno. Exponential approximations for the primitive equations of the ocean. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 425-440. doi: 10.3934/dcdsb.2007.7.425
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