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Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas
Duan, Renjun1; Huang, Feimin2,3; Wang, Yong2,3; Zhang, Zhu1
2019-11-01
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume234Issue:2Pages:925-1006
AbstractIn the paper, assuming that the motion of rarefied gases in a bounded domain is governed by the angular cutoff Boltzmann equation with diffuse reflection boundary, we study the effects of both soft intermolecular interaction and non-isothermal wall temperature upon the long-time dynamics of solutions to the corresponding initial boundary value problem. Specifically, we are devoted to proving the existence and dynamical stability of stationary solutions whenever the boundary temperature has suitably small variations around a positive constant. For the proof of existence, we introduce a new mild formulation of solutions to the steady boundary-value problem along the speeded backward bicharacteristic, and develop the uniform estimates on approximate solutions in both L2 and L 8. Such mild formulation proves to be useful for treating the steady problem with soft potentials even over unbounded domains. In showing the dynamical stability, a new point is that we can obtain the sub-exponential time-decay rate in L 8 without losing any velocity weight, which is actually quite different from the classical results, such as those in Caflisch (Commun Math Phys 74: 97-109, 1980) and Strain and Guo (Arch Ration Mech Anal 187: 287-339, 2008), for the torus domain and essentially due to the diffuse reflection boundary and the boundedness of the domain.
DOI10.1007/s00205-019-01405-5
Language英语
Funding ProjectCUHK[4053213] ; CUHK[14302817] ; National Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11688101] ; NSFC[11771429]
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000482386000011
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35605
Collection应用数学研究所
Corresponding AuthorDuan, Renjun
Affiliation1.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Duan, Renjun,Huang, Feimin,Wang, Yong,et al. Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2019,234(2):925-1006.
APA Duan, Renjun,Huang, Feimin,Wang, Yong,&Zhang, Zhu.(2019).Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,234(2),925-1006.
MLA Duan, Renjun,et al."Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 234.2(2019):925-1006.
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