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Low Froude number limit of the rotating shallow water and Euler equations


Author: Kung-Chien Wu
Journal: Proc. Amer. Math. Soc. 142 (2014), 939-947
MSC (2010): Primary 35B25, 35Q31, 76B15
DOI: https://doi.org/10.1090/S0002-9939-2013-11981-7
Published electronically: December 6, 2013
MathSciNet review: 3148528
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Abstract: We perform the mathematical derivation of the rotating lake equations (or anelastic system) from the classical solution of the rotating shallow water and Euler equations when the Froude number tends to zero.


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Additional Information

Kung-Chien Wu
Affiliation: Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 OWA, United Kingdom
Address at time of publication: Department of Mathematics, National Kaohsiung Normal University, 824 Kaohsiung, Taiwan
Email: kcwu@nknucc.nknu.edu.tw, kungchienwu@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11981-7
Keywords: Shallow water equations, Euler equations, low Froude number limit, incompressible limit, lake equations, anelastic system.
Received by editor(s): November 24, 2011
Received by editor(s) in revised form: April 13, 2012
Published electronically: December 6, 2013
Additional Notes: It is a pleasure to thank Professor Chi-Kun Lin for stimulating discussions concerning this paper. The author would also like to thank Dr. Clément Mouhot for his kind invitation to visit Cambridge during the 2011–2013 academic years.
This work is supported by the Tsz-Tza Foundation (Taiwan), National Science Council under Grant 102-2115-M-017-004-MY2 (Taiwan) and ERC Grant MATKIT (European Union)
Communicated by: Walter Craig
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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