Going beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases

Lingfei Li; Yingying Xie; Yongsheng Yan; Xiaoqiang Ma; Lingfei Li; Yingying Xie; Yongsheng Yan; Xiaoqiang Ma

doi:10.3934/math.2022555

AIMS Mathematics

2022, Volume 7, Issue 6: 9957-9975. doi: 10.3934/math.2022555

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Going beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases

1.
School of Economics and Management, Northwest University, Xi'an, Shannxi 710127, China
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shannxi 710049, China

Received: 29 October 2021 Revised: 21 February 2022 Accepted: 08 March 2022 Published: 21 March 2022
MSC : 35A01, 35D99

The present paper considers the blowup properties in trapped dipolar quantum gases modelled by the Gross-Pitaevskii equation. More precisely, through analyzing the temporal evolution of $ J'(t) $ in the form of uncertain principle ^[1], we provide some invariant evolution flows. Based on that, we establish the global existence versus blowup dichotomy of solutions above the mass-energy threshold. Meanwhile, we can estimate the behaviour of solutions with arbitrary large energy.
- trapped quantum gases,
- gross-pitaevskii equation,
- blowup dynamics,
- mass-energy threshold,
- arbitrary large energy
Citation: Lingfei Li, Yingying Xie, Yongsheng Yan, Xiaoqiang Ma. Going beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases[J]. AIMS Mathematics, 2022, 7(6): 9957-9975. doi: 10.3934/math.2022555

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Abstract

The present paper considers the blowup properties in trapped dipolar quantum gases modelled by the Gross-Pitaevskii equation. More precisely, through analyzing the temporal evolution of $ J'(t) $ in the form of uncertain principle ^[1], we provide some invariant evolution flows. Based on that, we establish the global existence versus blowup dichotomy of solutions above the mass-energy threshold. Meanwhile, we can estimate the behaviour of solutions with arbitrary large energy.

References

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