The Madelung equations of quantum mechanics suggest the hydrodynamic model of quantum mechanics (quantum mechanics is described as a fluid of universes in a multiverse, which, in the non-relativistic setting, is described by configuration space). However, the Madelung equations are Euler hydrodynamic equations, and Euler equations only describe bulk flow of a fluid. To get the full dynamics of a fluid, one can use a Lagrange description (among other solutions).
This suggests that the Madelung equations give an incomplete description of the hydrodynamic model of quantum mechanics, and a proper description of the hydrodynamic model would be (or be equivalent to) a Lagrange description.
Has anyone developed such a description?
(Note: I'm aware that the Bohmian mechanics an be derived from the Madelung equations by assuming that the universe fluid's particle velocity is equal to the bulk flow velocity. However, I've never seen any motivation for this assumption. I'd also be satisfied with a justification of why this works.)