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Two dimensional Gross-Pitaevskii equation with space-time white noise

Anne de Bouard 1 Arnaud Debussche 2, 3 Reika Fukuizumi 4 
3 MINGUS - Multi-scale numerical geometric schemes
ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique , IRMAR - Institut de Recherche Mathématique de Rennes
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 well-posedness of the model using an inhomogeneous Wick renormalization due to the potential, and prove the existence of an invariant measure and of stationary martingale solutions.
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Submitted on : Monday, February 15, 2021 - 2:49:15 PM
Last modification on : Tuesday, July 5, 2022 - 8:39:07 AM
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Anne de Bouard, Arnaud Debussche, Reika Fukuizumi. Two dimensional Gross-Pitaevskii equation with space-time white noise. International Mathematics Research Notices, Oxford University Press (OUP), 2022, ⟨10.1093/imrn/rnac137⟩. ⟨hal-03137755⟩



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