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arXiv · 2101.10106

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

Anne de Bouard·Arnaud Debussche·Reika Fukuizumi
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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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Anne de Bouard, Arnaud Debussche, Reika Fukuizumi. 2021-01-25. Two dimensional Gross-Pitaevskii equation with space-time white noise. https://arxiv.org/abs/2101.10106

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