International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), 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 G. Caviglia and A. Morro. 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.