Arnold's hydrodynamics revisited

الملخص EN

The purpose of this short paper is to revisit the infinite Lie group theoretical framework of hydrodynamics developed by V.

Arnold in 1966.

First of all, we extend this approach from the Lie pseudogroup of volume preserving transformations to an arbitrary Lie pseudogroup.

Then, by departing from Arnold’s purely analytic approach and adopting a purely formal point of view, we are able to recover the same results.

Finally, we provide the analogue for both the so-called “body” and “space” dynamical equations.

We conclude by showing that even this new approach can be superseded by dynamics on Lie groupoids, along ideas pioneered by the brothers E.

and F.

Cosserat or H.

Weyl, on the condition to change the underlying philosophy.