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Global attractor for a ginzburg-landau type model of rotating bose-einstein condensates
journal contributionposted on 2021-03-22, 18:12 authored by A Cheskidov, D Marahrens, C Sparber
© 2017 International Press. 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.
CitationCheskidov, A., Marahrens, D.Sparber, C. (2017). Global attractor for a ginzburg-landau type model of rotating bose-einstein condensates. Dynamics of Partial Differential Equations, 14(1), 5-32. https://doi.org/10.4310/DPDE.2017.v14.n1.a2
PublisherInternational Press of Boston