Blow up threshold for the Gross‐Pitaevskii system with trapped dipolar quantum gases

Liu, Baiyu; Ma, Li; Wang, Jing

doi:10.1002/zamm.201400189

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…Dimension reduction, ground states and dynamical properties of a condensate in anisotropic confinement were the subject of [4]. A sharp blowup threshold was given in [25], the case of a dipolar GPE system was studied in [22]. Stability of standing waves and their symmetry and orbits was studied in [11].…”

Section: Introductionmentioning

confidence: 99%

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Luo¹,

Stylianou²

2019

Preprint

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We study the following nonlocal mixed order Gross-Pitaevskii equationwhere K is the classical dipole-dipole interaction kernel, λ 3 > 0 and p ∈ (4, 6]; the case p = 6 being energy critical. For p = 5 the equation is considered currently as the stateof-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different parameter regimes; for p = 6 we prove global well-posedness and small data scattering.

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Section: Introductionmentioning

confidence: 99%

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Luo¹,

Stylianou²

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Dimension reduction, ground states and dynamical properties of a condensate in anisotropic confinement were the subject of [4]. A sharp blowup threshold was given in [26], the case of a dipolar GPE system was studied in [23]. Stability of standing waves and their symmetry and orbits was studied in [12].…”

mentioning

confidence: 99%

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Luo¹,

Stylianou²

2021

DCDS-B

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We study the following nonlocal mixed order Gross-Pitaevskii equation i ∂tψ = − 1 2 ∆ψ + Vext ψ + λ 1 |ψ| 2 ψ + λ 2 (K * |ψ| 2) ψ + λ 3 |ψ| p−2 ψ, where K is the classical dipole-dipole interaction kernel, λ 3 > 0 and p ∈ (4, 6]; the case p = 6 being energy critical. For p = 5 the equation is considered currently as the state-of-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different parameter regimes; for p = 6 we prove global well-posedness and small data scattering.

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Concentration of blow-up solutions for the Gross-Pitaveskii equation

Zhu

2024

Advances in Nonlinear Analysis

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We consider the blow-up solutions for the Gross-Pitaveskii equation modeling the attractive Boes-Einstein condensate. First, a new variational characteristic is established by computing the best constant of a generalized Gagliardo-Nirenberg inequality. Then, a lower bound on blow-up rate and a new concentration phenomenon of blow-up solutions are obtained in the L 2 {L}^{2} supercritical case. Finally, in the L 2 {L}^{2} critical case, a delicate limit of blow-up solutions is analyzed.

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Blow up threshold for the Gross‐Pitaevskii system with trapped dipolar quantum gases

Cited by 3 publications

References 20 publications

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Concentration of blow-up solutions for the Gross-Pitaveskii equation

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