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.