Analysis/Mathematical Physics Seminar

I will review recent progress on some dispersive type PDEs including the nonlinear magnetic and fractional Schroedinger equations with singular and unbounded potentials. This study is motivated by related open questions in the area in oder to understand the asymptotic behavior of solutions to a system where the nonlinearity might cause long-range effect. We will give a threshold condition on global existence and wave collapse for rotating Bose-Einstein condensation. We further prove the orbital stability for bound states that exhibit symmetries of vortex type that are signature phenomena for superfluidity as well as boson stars.