Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise

Anne de Bouard; Arnaud Debussche; Reika Fukuizumi

doi:10.1093/imrn/rnac137

Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise

Anne de Bouard
, Arnaud Debussche
, Reika Fukuizumi

UMR 6625
Tohoku University

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

In this paper we consider the two-dimensional stochastic Gross–Pitaevskii equation, which is a model to describe Bose–Einstein condensation at positive temperature. The equation is a complex Ginzburg–Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.

langue originale	Anglais
Pages (de - à)	10556-10614
Nombre de pages	59
journal	International Mathematics Research Notices
Volume	2023
Numéro de publication	12
Les DOIs	https://doi.org/10.1093/imrn/rnac137
état	Publié - 1 juin 2023

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10.1093/imrn/rnac137

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title = "Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise",

abstract = "In this paper we consider the two-dimensional stochastic Gross–Pitaevskii equation, which is a model to describe Bose–Einstein condensation at positive temperature. The equation is a complex Ginzburg–Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.",

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N2 - In this paper we consider the two-dimensional stochastic Gross–Pitaevskii equation, which is a model to describe Bose–Einstein condensation at positive temperature. The equation is a complex Ginzburg–Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.

AB - In this paper we consider the two-dimensional stochastic Gross–Pitaevskii equation, which is a model to describe Bose–Einstein condensation at positive temperature. The equation is a complex Ginzburg–Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.

UR - https://www.scopus.com/pages/publications/85145000472

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DO - 10.1093/imrn/rnac137

M3 - Article

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SN - 1073-7928

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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ER -

Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise

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