The Boltzmann equation with large-amplitude initial data in bounded domains

doi:10.1016/j.aim.2018.11.007

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	The Boltzmann equation with large-amplitude initial data in bounded domains
	Duan, Renjun 1; Wang, Yong2,3
刊名	ADVANCES IN MATHEMATICS
	2019-02-05
卷号	343 页码:36-109
关键词	Boltzmann equation Global well-posedness Bounded domain Large-amplitude initial data Diffuse reflection boundary A priori estimate
ISSN号	0001-8708
DOI	10.1016/j.aim.2018.11.007
英文摘要	The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class of non-negative initial data which have arbitrary large amplitude and even contain vacuum. The result shows that the oscillation of solutions away from global Maxwellians becomes small after some positive time provided that they are initially close to each other in L-2. This yields the disappearance of any initial vacuum and the exponential convergence of large amplitude solutions to equilibrium in large time. The isothermal diffuse reflection boundary condition plays a vital role in the analysis. The most key ingredients in our strategy of the proof include: (i) L-x,v(2)-(LxLv1)-L-infinity-L-x,v(infinity) estimates along a bootstrap argument; (ii) Pointwise estimates on the upper bound of the gain term by the product of L-infinity norm and L-2 norm; (iii) An iterative procedure on the nonlinear term. (C) 2018 Elsevier Inc. All rights reserved.
资助项目	General Research Fund from RGC of Hong Kong[409913] ; CUHK[3132699] ; National Natural Sciences Foundation of China[11771429] ; National Natural Sciences Foundation of China[11688101]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000457070500003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/32153]
专题	应用数学研究所
通讯作者	Duan, Renjun
作者单位	1.Chinese Univ Hong Kong, Dept Math, Hong Kong, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Duan, Renjun,Wang, Yong. The Boltzmann equation with large-amplitude initial data in bounded domains[J]. ADVANCES IN MATHEMATICS,2019,343:36-109.
APA	Duan, Renjun,&Wang, Yong.(2019).The Boltzmann equation with large-amplitude initial data in bounded domains.ADVANCES IN MATHEMATICS,343,36-109.
MLA	Duan, Renjun,et al."The Boltzmann equation with large-amplitude initial data in bounded domains".ADVANCES IN MATHEMATICS 343(2019):36-109.