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

Alexey Cheskidov, Daniel Marahrens, Christof Sparber
2017 Dynamics of Partial Differential Equations  
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
more » ... tain 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. Contents 14 5. Bounds on the mass and energy 18 6. The global attractor and its properties 21 Appendix A. Derivation of the kernel of the linear semi-group 28 References 31
doi:10.4310/dpde.2017.v14.n1.a2 fatcat:ecgvktw33nhclorfjfu7e5dwqi