Open AccessGoing beyond the threshold: Blowup criteria with arbitrary large energy in trapped quantum gases
Author(s) -
Lingfei Li,
Yingying Xie,
Yongsheng Yan,
Xiaoqiang Ma
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2022555
Subject(s) - quantum , invariant (physics) , energy (signal processing) , dipole , physics , mathematics , mathematical physics , quantum mechanics
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.