Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noise

被引：3
|
作者：
Peng, Xuhui [1 ,2 ]
Huang, Jianhua [3 ]
Zhang, Rangrang [4 ]
机构：
[1] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Peoples R China
[2] Hunan Normal Univ, Coll Hunan Prov, Key Lab Appl Stat & Data Sci, Changsha, Peoples R China
[3] Natl Univ Def Technol Changsha, Coll Sci, Changsha 410073, Peoples R China
[4] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 04期
关键词：
Exponential mixing; Malliavin calculus; Ergodic; Real Ginzburg-Landau equation; NAVIER-STOKES EQUATIONS; STOCHASTIC PDES; SYSTEMS; DRIVEN;
D O I：
10.1016/j.jde.2020.03.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stochastic forcing acting only in four directions. The main challenge is to establish time asymptotic smoothing properties of the Markovian dynamics corresponding to this system. To achieve this, we propose a condition which only requires four noises. (C) 2020 Elsevier Inc. All rights reserved.
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页码：3686 / 3720
页数：35
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