Vorträge und Posterpräsentationen (ohne Tagungsband-Eintrag):
A. Jüngel:
"Diffusion in macroscopic quantum models: drift-diffusion and Navier-Stokes approximations";
Vortrag: Workshop on Classical and Quantum Mechanical Models of Many-Particle Systems,
Oberwolfach (eingeladen);
05.12.2010
- 11.12.2010.
Kurzfassung deutsch:
Siehe englisches Abstract.
Kurzfassung englisch:
Quantum fluid models have been recently derived by Degond, Mehats, and
Ringhofer from the Wigner-BGK equation by a moment method with a
quantum Maxwellian closure. In the O(eps^4) approximation, where
eps is the scaled Planck constant, this leads to local quantum
diffusion or quantum hydrodynamic equations. In this talk, we present
recent results on the global existence and long-time decay of solutions
of these models.
First, we consider quantum diffusion models containing highly nonlinear
fourth-order or sixth-order differential operators. The existence
results are obtained from a priori estimates using entropy dissipation
methods. Second, a quantum Navier-Stokes model, derived by Brull and
Mehats, will be analyzed. This system contains nonlinear third-order
derivatives and a density-depending viscosity. The key idea of the
mathematical analysis is the reformulation of the system in terms of a
new "osmotic velocity" variable, leading to a viscous quantum
hydrodynamic model. Surprisingly, this variable has been also
successfully employed by Bresch and Desjardins in (non-quantum)
viscous Korteweg models.
Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.