Ergodicity of the 2D Navier-Stokes equations with degenerate multiplicative noise

doi:10.1007/s10255-018-0728-z

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	Ergodicity of the 2D Navier-Stokes equations with degenerate multiplicative noise
	Dong, Zhao1,3 ; Peng, Xu-hui 2
	2018
Source Publication	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
Volume	34 Issue:1 Pages:97-118
Abstract	Consider the two-dimensional, incompressible Navier-Stokes equations on torus T (2) = [-pi, pi](2) driven by a degenerate multiplicative noise in the vorticity formulation (abbreviated as SNS): dw (t) = nu Delta w (t) dt + B(Kw (t) ,w (t) )dt + Q(w (t) )dW (t) . We prove that the solution to SNS is continuous differentiable in initial value. We use the Malliavin calculus to prove that the semigroup {P (t) }(tae0) generated by the SNS is asymptotically strong Feller. Moreover, we use the coupling method to prove that the solution to SNS has a weak form of irreducibility. Under almost the same Hypotheses as that given by Odasso, Prob. Theory Related Fields, 140: 41-82 (2005) with a different method, we get an exponential ergodicity under a stronger norm.
Keyword	tochastic Navier-Stokes equation asymptotically strong Feller property ergodicity
DOI	10.1007/s10255-018-0728-z
Language	英语
Funding Project	Scientific Research Fund of Hunan Provincial Education Department[17C0953] ; NSFC[11501195] ; National Natural Science Foundation of China[11371041] ; National Natural Science Foundation of China[11431014] ; Construct Program of the Key Discipline in Hunan Province ; Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences[2008DP173182] ; Youth Scientific Research Fund of Hunan Normal University[Math140650]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied
WOS ID	WOS:000427057400008
Publisher	SPRINGER HEIDELBERG
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/29921
Collection	应用数学研究所
Corresponding Author	Peng, Xu-hui
Affiliation	1.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing, Peoples R China 2.Hunan Normal Univ, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Changsha 410081, Hunan, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
Recommended Citation GB/T 7714	Dong, Zhao,Peng, Xu-hui. Ergodicity of the 2D Navier-Stokes equations with degenerate multiplicative noise[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2018,34(1):97-118.
APA	Dong, Zhao,&Peng, Xu-hui.(2018).Ergodicity of the 2D Navier-Stokes equations with degenerate multiplicative noise.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,34(1),97-118.
MLA	Dong, Zhao,et al."Ergodicity of the 2D Navier-Stokes equations with degenerate multiplicative noise".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 34.1(2018):97-118.

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