MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION

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	MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION
	Huang, Feimin; Wang, Yong1
	2018-09-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	38 期号:5 页码:1549-1566
摘要	The regularity of solutions to the Boltzmann equation is a fundamental problem in the kinetic theory. In this paper, the case with angular cut-off is investigated. It is shown that the macroscopic parts of solutions to the Boltzmann equation, i.e., the density, momentum and total energy are continuous functions of (x, t) in the region R-3 x (0, +infinity). More precisely, these macroscopic quantities immediately become continuous in any positive time even though they are initially discontinuous and the discontinuities of solutions propagate only in the microscopic level. It should be noted that such kind of phenomenon can not happen for the compressible Navier-Stokes equations in which the initial discontinuities of the density never vanish in any finite time, see [22]. This hints that the Boltzmann equation has better regularity effect in the macroscopic level than compressible Navier-Stokes equations.
关键词	Boltzmann equation macroscopic regularity compressible Navier-Stokes equations
语种	英语
资助项目	National Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11371349] ; NSFC[11688101] ; NSFC[11771429]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000446808900006
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31485
专题	应用数学研究所
通讯作者	Wang, Yong
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Wang, Yong. MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION[J]. ACTA MATHEMATICA SCIENTIA,2018,38(5):1549-1566.
APA	Huang, Feimin,&Wang, Yong.(2018).MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION.ACTA MATHEMATICA SCIENTIA,38(5),1549-1566.
MLA	Huang, Feimin,et al."MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION".ACTA MATHEMATICA SCIENTIA 38.5(2018):1549-1566.