Dynamics of Partial Differential Equations
Volume 14 (2017)
Global attractor for a Ginzburg–Landau type model of rotating Bose–Einstein condensates
Pages: 5 – 32
We study the long time behavior of solutions to a nonlinear partial differential equation arising in the mean-field description of trapped rotating Bose–Einstein condensates. The equation can be seen as a hybrid between the well-known nonlinear Schrödinger/Gross–Pitaevskii equation and the Ginzburg–Landau equation. We prove existence and uniqueness of global in-time solutions in the physical energy space and establish the existence of a global attractor within the associated dynamics. We also obtain basic structural properties of the attractor and an estimate on its Hausdorff and fractal dimensions. As a by-product, we establish heat-kernel estimates on the linear part of the equation.
Gross–Pitaevskii equation, Bose–Einstein condensation, Ginzburg–Landau equation, vortices, global attractor
2010 Mathematics Subject Classification