Symmetries of Euler Equations in Lagrangian Coordinates

DOI

10.2991/jnmp.1996.3.1-2.24How to use a DOI?

Abstract

The transition from Eulerian to Lagrangian coordinates is a nonlocal transformation. In general, isomorphism should not take place between basic Lie groups of studied equations. Besides, in the case of plane and rotational symmetric motion hydrodynamic equations in Lagrangian coordinates are partially integrated. This fact introduces arbitrary functions, initial data, to the resulting systems and makes cuurently central the problem of group classification. It is stated that under a transition to Lagrangian coordinates, the main group becomes infinite­dimensional as well in space coordinates. The exclusive values of arbitrary functions of Lagrange coordinates (vorticity, momentum), at which the further group widening takes place, are found in [1].

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Victor Andreev
PY  - 1996
DA  - 1996/05/01
TI  - Symmetries of Euler Equations in Lagrangian Coordinates
JO  - Journal of Nonlinear Mathematical Physics
SP  - 196
EP  - 201
VL  - 3
IS  - 1-2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1996.3.1-2.24
DO  - 10.2991/jnmp.1996.3.1-2.24
ID  - Andreev1996
ER  -