ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS

doi:10.3934/cpaa.2021083

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	ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS
	Chen, Robin ming 1; Huang, F. E. I. M. I. N.2; Wang, D. E. H. U. A.1; Yuan, D. I. F. A. N.3,4
	2021-07-01
发表期刊	COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
ISSN	1534-0392
卷号	20 期号:7-8 页码:2519-2533
摘要	We are concerned with the stability of vortex sheet solutions for the two-dimensional nonisentropic compressible flows in elastodynamics. This is a nonlinear free boundary hyperbolic problem with characteristic discontinuities, which has extra difficulties when considering the effect of entropy. The addition of the thermal effect to the system makes the analysis of the Lopatinskii determinant extremely complicated. Our results are twofold. First, through a qualitative analysis of the roots of the Lopatinskii determinant for the linearized problem, we find that the vortex sheets are weakly stable in some supersonic and subsonic regions. Second, under the small perturbation of entropy, the nonlinear stability can be adapted from the previous two-dimensional isentropic elastic vortex sheets [6] by applying the Nash-Moser iteration. The two results confirm the strong elastic stabilization of the vortex sheets. In particular, our conditions for the linear stability (1) ensure that a stable supersonic regime as well as a stable subsonic one always persist for any given nonisentropic configuration, and (2) show how the stability condition changes with the thermal fluctuation. The existence of the stable subsonic bubble, a phenomenon not observed in the Euler flow, is specially due to elasticity.
关键词	Vortex sheets Elastodynamics contact discontinuities stability
DOI	10.3934/cpaa.2021083
收录类别	SCI
语种	英语
资助项目	NSF[DMS-1907519] ; NSF[DMS-1907584] ; National Center for Mathematics and Interdisciplinary Sciences, AMSS, CAS ; NSFC[12001045] ; NSFC[11371349] ; NSFC[11688101] ; China Scholarship Council[201704910503] ; China Postdoctoral Science Foundation[2020M680428]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000684207400006
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59078
专题	中国科学院数学与系统科学研究院
通讯作者	Wang, D. E. H. U. A.
作者单位	1.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 4.Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China
推荐引用方式 GB/T 7714	Chen, Robin ming,Huang, F. E. I. M. I. N.,Wang, D. E. H. U. A.,et al. ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2021,20(7-8):2519-2533.
APA	Chen, Robin ming,Huang, F. E. I. M. I. N.,Wang, D. E. H. U. A.,&Yuan, D. I. F. A. N..(2021).ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,20(7-8),2519-2533.
MLA	Chen, Robin ming,et al."ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 20.7-8(2021):2519-2533.