P. Fuchs, A. Jüngel, M. Von Renesse:
"On the Lagrangian structure of quantum fluid models";
Discrete And Continuous Dynamical Systems, 34 (2013), 4; S. 1375 - 1396.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
Some quantum
uid models are written as the Lagrangian
ow of
mass distributions and their geometric properties are explored. The rst model
includes magnetic e ects 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 di erent energy-dissipation identities is explained
by the de nition of the Noether currents.

Quantum hydrodynamics; quantum Navier-Stokes systems

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