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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 2, Pages 377-384

Conservation laws for incompressible fluids

1Department of Mathematics, Via L.B. Alberti 4, Genova 16132, Italy
2Department of Biophysical and Electronic Engineering, Viale Causa 13, Genova 16145, Italy

Received 18 November 1987

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By means of a direct approach, a complete set of conservation laws for incompressible fluids is determined. The problem is solved in the material (Lagrangian) description and the results are eventually rewritten in the spatial (Eulerian) formulation. A new infinite family of conservation laws is determined, besides those for linear momentum, angular momentum, energy and helicity.