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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	10556-10614
Number of pages	59
Journal	International Mathematics Research Notices
Volume	2023
Issue number	12
DOIs	https://doi.org/10.1093/imrn/rnac137
Publication status	Published - 1 Jun 2023

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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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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.

U2 - 10.1093/imrn/rnac137

DO - 10.1093/imrn/rnac137

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EP - 10614

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

Abstract

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