ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS

doi:10.3934/cpaa.2021083

	ON THE STABILITY OF TWO-DIMENSIONAL NONISENTROPIC ELASTIC VORTEX SHEETS
	Chen, Robin ming 4; Huang, F. E. I. M. I. N.3; Wang, D. E. H. U. A.4; Yuan, D. I. F. A. N.1,2
刊名	COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
	2021-07-01
卷号	20 期号:7-8 页码:2519-2533
关键词	Vortex sheets Elastodynamics contact discontinuities stability
ISSN号	1534-0392
DOI	10.3934/cpaa.2021083
英文摘要	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.
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
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000684207400006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59077]
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.Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China 2.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 4.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
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.