Stability of Couette flow for 2D Boussinesq system with vertical dissipation

doi:10.1016/j.jfa.2021.109255

CSpace

	Stability of Couette flow for 2D Boussinesq system with vertical dissipation
	Deng, Wen 1,2; Wu, Jiahong 3; Zhang, Ping 1,2,4
	2021-12-15
发表期刊	JOURNAL OF FUNCTIONAL ANALYSIS
ISSN	0022-1236
卷号	281 期号:12 页码:40
摘要	This paper establishes the nonlinear stability of the Couette flow for the 2D Boussinesq equations with only vertical dissipation. The Boussinesq equations concerned here model buoyancy-driven fluids such as atmospheric and oceanographic flows. Due to the presence of the buoyancy forcing, the energy of the standard Boussinesq equations could grow in time. It is the enhanced dissipation created by the linear non-self-adjoint operator y partial derivative(x) - nu partial derivative(yy) in the perturbation equation that makes the nonlinear stability possible. When the initial perturbation from the Couette flow (y, 0) is no more than the viscosity to a suitable power (in the Sobolev space H-b with b > 4/3), we prove that the solution of the 2D Boussinesq system with only vertical dissipation on T x R remains close to the Couette at the same order. A special consequence of this result is the stability of the Couette for the 2D Navier-Stokes equations with only vertical dissipation. (C) 2021 Elsevier Inc. All rights reserved.
关键词	Boussinesq equations Enhanced dissipation Stability of Couette flow
DOI	10.1016/j.jfa.2021.109255
收录类别	SCI
语种	英语
资助项目	K. C. Wong Education Foundation ; National Science Foundation of USA[DMS 2104682] ; AT&T Foundation at Oklahoma State University ; NSF of China[11731007] ; NSF of China[12031006] ; NSF of China[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000709430900003
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59426
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Ping
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100049, Peoples R China 3.Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Deng, Wen,Wu, Jiahong,Zhang, Ping. Stability of Couette flow for 2D Boussinesq system with vertical dissipation[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2021,281(12):40.
APA	Deng, Wen,Wu, Jiahong,&Zhang, Ping.(2021).Stability of Couette flow for 2D Boussinesq system with vertical dissipation.JOURNAL OF FUNCTIONAL ANALYSIS,281(12),40.
MLA	Deng, Wen,et al."Stability of Couette flow for 2D Boussinesq system with vertical dissipation".JOURNAL OF FUNCTIONAL ANALYSIS 281.12(2021):40.