Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas

doi:10.1007/s00205-019-01405-5

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	Effects of Soft Interaction and Non-isothermal Boundary Upon Long-Time Dynamics of Rarefied Gas
	Duan, Renjun 2; Huang, Feimin1,3 ; Wang, Yong1,3 ; Zhang, Zhu 2
刊名	ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
	2019-11-01
卷号	234 期号:2 页码:925-1006
ISSN号	0003-9527
DOI	10.1007/s00205-019-01405-5
英文摘要	In 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.
资助项目	CUHK[4053213] ; CUHK[14302817] ; National Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11688101] ; NSFC[11771429]
WOS研究方向	Mathematics ; Mechanics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000482386000011
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35604]
专题	应用数学研究所
通讯作者	Duan, Renjun
作者单位	1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 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.