Journal of Nonlinear Mathematical Physics

Volume 19, Issue Supplement 1, November 2012, Pages 1 - 12

Variational Derivation of the Green–Naghdi Shallow-Water Equations

Authors
Delia Ionescu-Kruse
Institute of Mathematics of the Romanian Academy, Research Unit No. 6, P. O. Box 1-764, 014700 Bucharest, Romania,Delia.Ionescu@imar.ro
Received 22 March 2012, Accepted 13 May 2012, Available Online 28 November 2012.
DOI
10.1142/S1402925112400013How to use a DOI?
Keywords
Green–Naghdi equations; shallow-water waves; variational methods
Abstract

We consider the two-dimensional irrotational water-wave problem with a free surface and a flat bottom. In the shallow-water regime and without smallness assumption on the wave amplitude we derive, by a variational approach in the Lagrangian formalism, the Green–Naghdi equations (1.1). The second equation in (1.1) is a transport equation, the free surface is advected by the fluid flow. We show that the first equation of the system (1.1) yields the critical points of an action functional in the space of paths with fixed endpoints, within the Lagrangian formalism.

Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - Supplement 1
Pages
1 - 12
Publication Date
2012/11/28
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925112400013How to use a DOI?
Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Delia Ionescu-Kruse
PY  - 2012
DA  - 2012/11/28
TI  - Variational Derivation of the Green–Naghdi Shallow-Water Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 12
VL  - 19
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112400013
DO  - 10.1142/S1402925112400013
ID  - Ionescu-Kruse2012
ER  -