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Article Dans Une Revue International Mathematics Research Notices Année : 2022

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

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 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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Dates et versions

hal-03137755 , version 1 (15-02-2021)

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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, 2022, ⟨10.1093/imrn/rnac137⟩. ⟨hal-03137755⟩
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