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Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime
Chen, Gui-Qiang G.1,2,3; Secchi, Paolo4; Wang, Tao4,5,6
2019-05-01
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume232Issue:2Pages:591-695
AbstractWe 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.
DOI10.1007/s00205-018-1330-5
Language英语
Funding ProjectUK 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 Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000462144500002
PublisherSPRINGER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34224
Collection中国科学院数学与系统科学研究院
Corresponding AuthorChen, Gui-Qiang G.
Affiliation1.Univ Oxford, Math Inst, Oxford OX2 6GG, England
2.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China
3.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China
4.Univ Brescia, DICATAM, Math Div, I-25133 Brescia, Italy
5.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
6.Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Hubei, Peoples R China
Recommended Citation
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.
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