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P. Fuchs, A. Jüngel, M. Von Renesse:
"On the Langrangian sructure of quantum flud models";
in: "ASC Report 35/2011", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2011, ISBN: 978-3-902627-04-9.

Some quantum fluid models are written as the Lagrangian flow of mass distributions
and their geometric properties are explored. The first model includes magnetic effects and leads,
via the Madelung transform, to the electromagnetic Schr¨odinger equation in the Madelung representation.
It is shown that the Madelung transform is a symplectic map between Hamiltonian
systems. The second model is obtained from the Euler-Lagrange equations with friction induced
from a quadratic dissipative potential. This model corresponds to the quantum Navier-Stokes
equations with density-dependent viscosity. The fact that this model possesses two different
energy-dissipation identities is explained by the definition of the Noether currents.

http://www.asc.tuwien.ac.at/preprint/2011/asc35x2011.pdf