One of the key issues related to superfluidity is the existence of vortices. In very recent experiments on Bose-Einstein condensates, vortices have been observed in various conditions. This monograph is dedicated to the mathematical modelling of these phenomena. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. The mathematical analysis is made in the framework of the Gross-Pitaevskii energy. Results are presented and open problems related to recent experiments are explained.

The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum condensates, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments.

Inhalt
The Physical Experiment and Their Mathematical Modeling.- The Mathematical Setting: A Survey of the Main Theorems.- Two-Dimensional Model for otating Condensate.- Other Trapping Potentials.- High-Velocity and Quantam Hall Regime.- Three-Dimensional Rotating Condensate.- Superfluid Flow Around an Obstacle.- Further Open Problems.