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

被引：1
|
作者：
de Bouard, Anne [1 ]
Debussche, Arnaud [2 ,3 ]
Fukuizumi, Reika [4 ]
机构：
[1] Ecole Polytech, CMAP, CNRS, IP Paris, F-91128 Palaiseau, France
[2] Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France
[3] Inst Univ France, Paris, France
[4] Tohoku Univ, Grad Sch Informat Sci, Res Ctr Pure & Appl Math, Sendai, Miyagi 9808579, Japan
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 12期
关键词：
GLOBAL WELL-POSEDNESS; SCHRODINGER-OPERATORS; DYNAMICS;
D O I：
10.1093/imrn/rnac137
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：10556 / 10614
页数：59
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