Publications in Scientific Journals:
P. Fuchs, A. Jüngel, M. Von Renesse:
"On the Lagrangian structure of quantum fluid models";
Discrete And Continuous Dynamical Systems,
34
(2013),
4;
1375
- 1396.
English abstract:
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.
German abstract:
Siehe englisches Abstract.
Keywords:
Quantum hydrodynamics; quantum Navier-Stokes systems
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.3934/dcds.2014.34.1375
Created from the Publication Database of the Vienna University of Technology.