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MACROSCOPIC REGULARITY FOR THE BOLTZMANN EQUATION
Huang, Feimin; Wang, Yong1
2018-09-01
Source PublicationACTA MATHEMATICA SCIENTIA
ISSN0252-9602
Volume38Issue:5Pages:1549-1566
AbstractThe 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.
KeywordBoltzmann equation macroscopic regularity compressible Navier-Stokes equations
Language英语
Funding ProjectNational Center for Mathematics and Interdisciplinary Sciences ; AMSS ; CAS ; NSFC[11371349] ; NSFC[11688101] ; NSFC[11771429]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000446808900006
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31485
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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