KMS Of Academy of mathematics and systems sciences, CAS
| Stability of Couette flow for 2D Boussinesq system with vertical dissipation | |
| Deng, Wen1,2; Wu, Jiahong3; Zhang, Ping1,2,4 | |
| 2021-12-15 | |
| Source Publication | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| ISSN | 0022-1236 |
| Volume | 281Issue:12Pages:40 |
| Abstract | 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. |
| Keyword | Boussinesq equations Enhanced dissipation Stability of Couette flow |
| DOI | 10.1016/j.jfa.2021.109255 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000709430900003 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59426 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhang, Ping |
| Affiliation | 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 |
| Recommended Citation 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. |
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