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Long-time behavior of a Bose-Einstein equation in a two-dimensional thin domain

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  • We study the long-time behavior of the solutions to a nonlinear Schrödinger equation with a zero order dissipation and a quadratic potential when they are driven by an external force on a thin canal. We show that this behavior is described by a regular attractor which captures all the trajectories and have a finite Fractal dimension.
    Mathematics Subject Classification: Primary: 35L05, 35Q55; Secondary: 76B03.


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