A. Jüngel:

"Modeling and analysis of diffusive quantum fluid equations";

Talk: Workshop Theory and numerics for nonlinear Schroedinger equations, Nizza, Universität Nizza (invited); 2015-01-12 - 2015-01-14.

Quantum fluid equations are an interesting alternative to more sophisticated but computationally very expensive quantum transport models. In this talk, two classes of quantum fluid models are analyzed: quantum drift-diffusion and quantum Navier-Stokes equations. These models can be formally derived from a collisional Wigner equation in the diffusion limit. The quantum Navier-Stokes equations can be also obtained from a dissipative Euler-Lagrange equation with a quantum action functional on the space of probability measures, which allows one to relate quantum fluid models with the (one-particle) Schroedinger equation. The main mathematical challenge of the diffusive quantum models is the treatment of the highly nonlinear higher-order differential operators. The existence of global weak solutions is proved by using new analytical tools like entropy methods, systematic integration of parts, and osmotic velocity variable transformation.

Created from the Publication Database of the Vienna University of Technology.