Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise-Reference-Cited by-同舟云学术

Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise

Published:2022-05-31 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

de Bouard Anne¹,Debussche Arnaud²³,Fukuizumi Reika⁴

Affiliation:

1. CMAP, CNRS , Ecole polytechnique, I.P. Paris 91128 Palaiseau, France

2. Univ Rennes , CNRS, IRMAR–UMR 6625, F-35000 Rennes, France

3. Institut Universitaire de France

4. Research Center for Pure and Applied Mathematics , Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac137/43905747/rnac137.pdf

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