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Exponential approximations for the primitive equations of the ocean

Temam, Roger M.; Wirosoetisno, Djoko

Authors

Roger M. Temam



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.

Citation

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

Journal Article Type Article
Publication Date 2007-03
Deposit Date Feb 29, 2008
Journal Discrete and Continuous Dynamical Systems - Series B
Print ISSN 1531-3492
Electronic ISSN 1553-524X
Publisher American Institute of Mathematical Sciences (AIMS)
Peer Reviewed Peer Reviewed
Volume 7
Issue 2
Pages 425-440
DOI https://doi.org/10.3934/dcdsb.2007.7.425
Keywords Singular perturbation, Exponential asymptotics, Gevrey regularity, Primitive equations.
Publisher URL http://www.aimsciences.org/journals/pdfs.jsp?paperID=2142&mode=abstract

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