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NONLINEAR STABILITY AND EXISTENCE OF VORTEX SHEETS FOR INVISCID LIQUID-GAS TWO-PHASE FLOW
Huang, Feimin1; Wang, Dehua2; Yuan, Difan3,4
2019-06-01
Source PublicationDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN1078-0947
Volume39Issue:6Pages:3535-3575
AbstractWe are concerned with the vortex sheet solutions for the inviscid two-phase flow in two dimensions. In particular, the nonlinear stability and existence of compressible vortex sheet solutions under small perturbations are established by using a modification of the Nash-Moser iteration technique, where a priori estimates for the linearized equations have a loss of derivatives. Due to the jump of the normal derivatives of densities of liquid and gas, we obtain the normal estimates in the anisotropic Sobolev space, instead of the usual Sobolev space. New ideas and techniques are developed to close the energy estimates and derive the tame estimates for the two-phase flows.
KeywordInviscid liquid-gas two-phase flow vortex sheets Nash-Moser scheme loss of derivatives nonlinear stability
DOI10.3934/dcds.2019146
Language英语
Funding ProjectNational Center for Mathematics and Interdisciplinary Sciences, AMSS, CAS ; NSFC[11371349] ; NSFC[11688101] ; NSF[DMS-1312800] ; NSF[DMS-1613213] ; China Scholarship Council[201704910503]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000459954800023
PublisherAMER INST MATHEMATICAL SCIENCES-AIMS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/33457
Collection应用数学研究所
Corresponding AuthorYuan, Difan
Affiliation1.Acad Sinica, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
2.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Huang, Feimin,Wang, Dehua,Yuan, Difan. NONLINEAR STABILITY AND EXISTENCE OF VORTEX SHEETS FOR INVISCID LIQUID-GAS TWO-PHASE FLOW[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2019,39(6):3535-3575.
APA Huang, Feimin,Wang, Dehua,&Yuan, Difan.(2019).NONLINEAR STABILITY AND EXISTENCE OF VORTEX SHEETS FOR INVISCID LIQUID-GAS TWO-PHASE FLOW.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,39(6),3535-3575.
MLA Huang, Feimin,et al."NONLINEAR STABILITY AND EXISTENCE OF VORTEX SHEETS FOR INVISCID LIQUID-GAS TWO-PHASE FLOW".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 39.6(2019):3535-3575.
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