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The convergence of Hamiltonian structure in the shallow water approximation

Ge, Zhong and Kruse, Hans Peter and Marsden, Jerrold E. and Scovel, Clint (1995) The convergence of Hamiltonian structure in the shallow water approximation. Canadian Applied Mathematics Quarterly, 3 (3). pp. 277-302. ISSN 1073-1849. http://resolver.caltech.edu/CaltechAUTHORS:20100810-072428335

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Abstract

It is shown that the Hamiltonian structure of the shallow water equations is, in a precise sense, the limit of the Hamiltonian structure for that of a three-dimensional ideal fluid with a free boundary problem as the fluid thickness tends to zero. The procedure fits into an emerging general scheme of convergence of Hamiltonian structures as parameters tend to special values. The main technical difficulty in the proof is how to deal with the condition of incompressibility. This is treated using special estimates for the solution of a mixed Dirichlet-Neumann problem for the Laplacian in a thin domain.


Item Type:Article
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http://www.math.ualberta.ca/ami/CAMQ/table_of_content/vol_3/3_3c.htmPublisherUNSPECIFIED
Additional Information:© 1995 Rocky Mountain Mathematics Consortium. Received by the editors in revised form on April 17, 1995. The first author was supported by the Ministry of Colleges and Universities of Ontario and the Natural Sciences and Engineering Research Council of Canada. Research of the second author was partially supported by the Humboldt Foundation. Research of the third author was partially supported by DOE contract DEFG03- 92ER-25129, a Fairchild Fellowship, and Fields Institute for Research in the Mathematical Sciences.
Funders:
Funding AgencyGrant Number
Ministry of Colleges and Universities of OntarioUNSPECIFIED
Natural Sciences and Engineering Research Council of CanadaUNSPECIFIED
Humboldt FoundationUNSPECIFIED
Department of EnergyDEFG03-92ER-25129
Fairchild FellowshipUNSPECIFIED
Fields Institute for Research in the Mathematical SciencesUNSPECIFIED
Record Number:CaltechAUTHORS:20100810-072428335
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100810-072428335
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ID Code:19352
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Deposited By: Ruth Sustaita
Deposited On:10 Aug 2010 20:44
Last Modified:26 Dec 2012 12:18

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