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Research Article | Open Access

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

Lingfei Li1, Yingying Xie2, Yongsheng Yan1, Xiaoqiang Ma1( )
School of Economics and Management, Northwest University, Xi'an, Shannxi 710127, China
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, Shannxi 710049, China
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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.

Keywords

trapped quantum gasesgross-pitaevskii equationblowup dynamicsmass-energy thresholdarbitrary large energy
CLC number: 35A01, 35D99

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AIMS Mathematics
Volume 7 Issue 6,
June 2022
Pages 9957-9975
DOI: 10.3934/math.2022555

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Cite this article:
Li L, Xie Y, Yan Y, et al. Going beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases. AIMS Mathematics, 2022, 7(6): 9957-9975. https://doi.org/10.3934/math.2022555

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Received: 29 October 2021
Revised: 21 February 2022
Accepted: 08 March 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)