[1]王 颜,陈光淦*,汪 品.带乘性退化噪声的准地转流方程的遍历[J].四川师范大学学报(自然科学版),2019,(06):763-769.[doi:10.3969/j.issn.1001-8395.2019.06.008]
 WANG Yan,CHEN Guanggan,WANG Pin.Ergodicity of Stochastic Quasi-geostrophic Flows Equations with a Degenerate Multiplicative Noise[J].Journal of SichuanNormal University,2019,(06):763-769.[doi:10.3969/j.issn.1001-8395.2019.06.008]
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带乘性退化噪声的准地转流方程的遍历()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年06期
页码:
763-769
栏目:
基础理论
出版日期:
2019-11-04

文章信息/Info

Title:
Ergodicity of Stochastic Quasi-geostrophic Flows Equations with a Degenerate Multiplicative Noise
文章编号:
1001-8395(2019)06-0763-07
作者:
王 颜 陈光淦* 汪 品
四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
WANG Yan CHEN Guanggan WANG Pin
College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
随机准地转流方程 遍历 退化噪声 渐近强Feller 性 不可约性
Keywords:
stochastic quasi-geostrophic equations ergodicity degenerate noise asymptotically strong Feller property irreducibility
分类号:
O175.2
DOI:
10.3969/j.issn.1001-8395.2019.06.008
文献标志码:
A
摘要:
带有界乘性退化噪声的随机准地转流方程是地球物理流体力学和海洋大气科学中的一类重要数学模型.由于有界乘性退化噪声的扰动,使得其所对应的Malliavin协方差算子不可逆,从而导致系统转移概率半群的强Feller性不满足.运用渐近强Feller性来克服退化噪声带来的困难,最终获得系统的遍历性.
Abstract:
This paper is concerned with the stochastic quasi-geostrophic flows equation with a bounded multiplicative degenerate noise.It is a kind of important mathematical model in geophysical fluid mechanics and marine atmospheric science.Due to the perturbation of the bounded multiplicative degenerate noise, the corresponding Malliavin covariance operator is invertible, which causes that the strong Feller property of the probability transition semigroups can not be applied.In this paper, we will use the asymptotically strong Feller property to overcome the difficulties caused by the degenerate noise, and finally obtain the ergodicity of the system.

参考文献/References:

[1] GRIFFA A, CASTELLARI S.Nonlinear general circulation of an ocean model driven by wind with a stochastic component[J].J Marine Research,1991,49(1):53-73.
[2] HOLLOWAY G.Ocean circulation:flow in probability under statistical dynamical forcing[J].Stochastic Models in Geosystems,1997,626(85):1925-1936.
[3] SAMELSON R M.Stochastically forced current fluctuations in vertical shear and over topography[J].J Geophysical Research Oceans,1989,94(6):8207-8215.
[4] DUAN J Q, BRANNAN J R, ERVIN V J.Escape probability, mean residence time and geophysical fluid particle dynamics[J].Physica D:Nonlinear Phenomena,1999,133(4):23-33.
[5] BRANNAN J R, DUAN J Q, WANNER T.Dissipative quasi-geostrophic dynamics under random forcing[J].J Mathematical Analysis and Applications,1998,228(1):221-233.
[6] DUAN J Q, GOLDYS B.Ergodicity of stochastically forced large scale geophysical flows[J].International J Molecular Medical Science 2001,28(6):313-320.
[7] HAIRER M, MATTINGLY J C.Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing[J].Annals of Mathematics,2006,164(3):993-1032.
[8] ROCKNER M, ZHANG X C.Stochastic tamed 3D Navier-Stokes equations:existence, uniqueness and ergodicity[J].Probability Theory and Related Fields,2009,145(2):211-267.
[9] ROMITO M.Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise[J].J Statistical Physics,2004,114(2):155-177.
[10] PU X K, GUO B L.Momentum estimates and ergodicity for the 3D stochastic cubic Ginzburg-Landau equation with degenerate noise[J].J Diff Eqns,2011,251(7):1747-1777.
[11] SHEN T L, HUANG J H.Ergodicity of 2D stochastic Ginzburg-Landau-Newell equations driven by degenerate noise[J].Mathematical Methods in the Applied Sciences,2017,40(13):4812-4831.
[12] YANG L, PU X K.Ergodicity of large scale stochastic geophysical flows with degenerate Gaussian noise[J].Applied Mathematics Letters,2017,64(1):27-33.
[13] CONSTANTIN P, POIAS C.Navier-Stokes Equations,Edition[M].Chicago:University of Chicago Press,1988.

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备注/Memo

备注/Memo:
收稿日期:2017-12-14 接受日期:2018-07-09 基金项目:国家自然科学基金(11571245) *通信作者简介:陈光淦(1978—),男,教授,主要从事随机偏微分方程的研究,Email:chenguanggan@hotmail.com
更新日期/Last Update: 2019-11-04