In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.
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@article{CRMECA_2018__346_3_175_0,
author = {Denis Serre},
title = {Helicity and other conservation laws in perfect fluid motion},
journal = {Comptes Rendus. M\'ecanique},
pages = {175--183},
publisher = {Elsevier},
volume = {346},
number = {3},
year = {2018},
doi = {10.1016/j.crme.2017.12.001},
language = {en},
}
Denis Serre. Helicity and other conservation laws in perfect fluid motion. Comptes Rendus. Mécanique, Volume 346 (2018) no. 3, pp. 175-183. doi : 10.1016/j.crme.2017.12.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.001/
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