Dr. Christof Sparber (Centre of Mathematical Sciences University of Cambridge, UK)

On the Gross-Pitaevskii equation for trapped dipolar quantum gases

I report on a recent joint work together with R. Carles and P. Markowich, where we consider the time-dependent Gross-Pitaevskii equation modeling Bose-Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension-reduction for this nonlinear and nonlocal Schrödinger equation.