Contributions to Books:
A. Jüngel, J. Milisic:
"Quantum Navier-Stokes equations";
in: "ASC Report 22/2010",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
Compressible Navier-Stokes models for quantum fluids are reviewed.
They are derived from a collisional Wigner equation by a moment method and a
Chapman-Enskog expansion around the quantum equilibrium. Introducing a new
velocity variable, the barotropic quantum Navier-Stokes model can be reformulated
as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional.
This functional provides a priori estimates which are exploited to prove the
global-in-time existence of weak solutions for general initial data. Furthermore, new
numerical results for the isothermal model are presented.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.