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arXiv · 1506.04706

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

Alexey Cheskidov·Daniel Marahrens·Christof Sparber
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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.

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Alexey Cheskidov, Daniel Marahrens, Christof Sparber. 2015-06-15. Global attractor for a Ginzburg-Landau type model of rotating Bose-Einstein condensates. https://arxiv.org/abs/1506.04706

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