Global attractor for a Ginzburg-Landau type model of rotating Bose-Einstein condensates

TL;DR

This paper investigates the long-term dynamics of a hybrid nonlinear PDE modeling rotating Bose-Einstein condensates, establishing the existence of a global attractor and analyzing its properties.

Contribution

It proves existence and uniqueness of global solutions and demonstrates the existence of a global attractor with structural properties for the model.

Findings

Existence and uniqueness of global solutions

Existence of a global attractor with structural properties

Estimates on the Hausdorff and fractal dimensions of the attractor

Abstract

We study the long time behavior of solutions to a nonlinear partial differential equation arising in the description of trapped rotating Bose-Einstein condensates. The equation can be seen as a hybrid between the well-known nonlinear Schr\"odinger/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.