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

doi:10.1016/j.aim.2018.11.007

CSpace > 应用数学研究所

	The Boltzmann equation with large-amplitude initial data in bounded domains
	Duan, Renjun 1; Wang, Yong2,3
	2019-02-05
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	343 页码:36-109
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.
关键词	Boltzmann equation Global well-posedness Bounded domain Large-amplitude initial data Diffuse reflection boundary A priori estimate
DOI	10.1016/j.aim.2018.11.007
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000457070500003
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32154
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.