Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime

doi:10.1007/s00205-018-1330-5

	Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime
	Chen, Gui-Qiang G.4,5,6; Secchi, Paolo 3; Wang, Tao 1,2,3
刊名	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
	2019-05-01
卷号	232 期号:2 页码:591-695
ISSN号	0003-9527
DOI	10.1007/s00205-018-1330-5
英文摘要	We are concerned with the nonlinear stability of vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. This is a nonlinear hyperbolic problem with a characteristic free boundary. In this paper, we introduce a new symmetrization by choosing appropriate functions as primary unknowns. A necessary and sufficient condition for the weakly linear stability of relativistic vortex sheets is obtained by analyzing the roots of the Lopatinski determinant associated to the constant coefficient linearized problem. Under this stability condition, we show that the variable coefficient linearized problem obeys an energy estimate with a loss of derivatives. The construction of certain weight functions plays a crucial role in absorbing the error terms caused by microlocalization. Based on the weakly linear stability result, we establish the existence and nonlinear stability of relativistic vortex sheets under small initial perturbations by a Nash-Moser iteration scheme.
资助项目	UK Engineering and Physical Sciences Research Council[EP/E035027/1] ; UK Engineering and Physical Sciences Research Council[EP/L015 811/1] ; Royal Society-Wolfson Research Merit Award (UK) ; Italian research projects[PRIN 2012L5WXHJ-004] ; Italian research projects[PRIN 2015YCJY3A-004] ; NSFC[11601398] ; NSFC[11731008]
WOS研究方向	Mathematics ; Mechanics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000462144500002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34223]
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-Qiang G.
作者单位	1.Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China 2.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 3.Univ Brescia, DICATAM, Math Div, I-25133 Brescia, Italy 4.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China 5.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China 6.Univ Oxford, Math Inst, Oxford OX2 6GG, England
推荐引用方式 GB/T 7714	Chen, Gui-Qiang G.,Secchi, Paolo,Wang, Tao. Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2019,232(2):591-695.
APA	Chen, Gui-Qiang G.,Secchi, Paolo,&Wang, Tao.(2019).Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,232(2),591-695.
MLA	Chen, Gui-Qiang G.,et al."Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 232.2(2019):591-695.