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

2021/01/25 by de Bouard, Anne, Debussche, Arnaud, Fukuizumi, Reika · 2 citations
#35Q55 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.10106

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.

Cited by

• Standing waves of the Anderson-Gross-Pitaevskii equation
• Large deviation principles for the Gross Pitaevskii Gibbs measure at low temperature

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