Limit behavior of attractive Bose-Einstein condensates passing an obstacle

In this paper, we mainly investigate ground states of trapped attractive Bose-Einstein condensates (BEC) passing an obstacle in the plane, which can be described by an L2-critical constraint minimization problem in an exterior domain Ω=R2∖ω, where the bounded convex domain ω⊂R2 with smooth boundary...

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Bibliographic Details
Published in:Journal of Differential Equations 2021-01, Vol.272, p.370-398
Main Authors: Deng, Yinbin, Guo, Yujin, Xu, Liangshun
Format: Article
Language:English
Subjects:
Blow-up behavior
Bose-Einstein condensates
Exterior domains
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Summary:In this paper, we mainly investigate ground states of trapped attractive Bose-Einstein condensates (BEC) passing an obstacle in the plane, which can be described by an L2-critical constraint minimization problem in an exterior domain Ω=R2∖ω, where the bounded convex domain ω⊂R2 with smooth boundary denotes the region of the obstacle. It is shown that minimizers (i.e. ground states) exist, if and only if the interaction strength a satisfies a0 is the unique positive radial solution of Δu−u+u3=0 in R2. If the trapping potential V(x) attains its global minima only along the whole boundary ∂Ω, the limit behavior of minimizers is analyzed as a↗a⁎ by employing the Pohozaev identity and the delicate energy analysis, where the mass concentration occurs at the flattest critical point of V(x) on ∂Ω.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.10.002