## IMA Postdoc Seminar (April 27, 2010)

**Speaker:**Lee, Chiun-Chang (Department of Mathematics, National Taiwan University)

**Title:**Compressible and incompressible limits of two-component Gross-Pitaevskii equations
with rotating fields and trap potentials.

**Abstract:** In this talk I will discuss the hydrodynamic limits including
the incompressible and the compressible limits of two-component
Gross-Pitaevskii equations with rotating fields and trap potentials.
The complex dynamics and the turbulent relaxation have been observed
in a rotating Bose-Einstein condensate depicted by a Gross-Pitaevskii
equation coupled with a rotating field and a trap potential. To see the
complex dynamics and the turbulent relaxation of two-component rotating
Bose-Einstein condensates, we study the hydrodynamic limits of two-component
systems of Gross-Pitaevskii equations in two spatial dimensions. We define
"H-function" a modulated energy functional which may control the propagation
of densities and linear momentums.