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Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System
Li, Hailiang1,2; Wang, Yi2,3,4; Yang, Tong5; Zhong, Mingying6
2018-04-01
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume228Issue:1Pages:39-127
AbstractThe main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.
DOI10.1007/s00205-017-1185-1
Language英语
Funding ProjectNNSFC[11231006] ; NNSFC[11671384] ; NNSFC[11225102] ; NNSFC[11301094] ; NNFC-RGC Grant[11461161007] ; Beijing New Century Baiqianwan Talent Project ; National Natural Sciences Foundation of China[11671385] ; Youth Innovation Promotion Association of CAS ; Young top-notch talent Program ; General Research Fund of Hong Kong[CityU 11302215] ; Beijing Postdoctoral Research Foundation[2014ZZ-96]
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000423111600002
PublisherSPRINGER
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29325
Collection应用数学研究所
Affiliation1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
2.Beijing Ctr Math & Informat Sci, Beijing 100048, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, HCMS,CEMS, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
5.City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
6.Guangxi Univ, Dept Math, Nanning, Peoples R China
Recommended Citation
GB/T 7714
Li, Hailiang,Wang, Yi,Yang, Tong,et al. Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2018,228(1):39-127.
APA Li, Hailiang,Wang, Yi,Yang, Tong,&Zhong, Mingying.(2018).Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,228(1),39-127.
MLA Li, Hailiang,et al."Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 228.1(2018):39-127.
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