HYDRODYNAMIC LIMIT OF THE BOLTZMANN EQUATION TO THE PLANAR RAREFACTION WAVE IN THREE DIMENSIONAL SPACE

doi:10.1137/20M1362905

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	HYDRODYNAMIC LIMIT OF THE BOLTZMANN EQUATION TO THE PLANAR RAREFACTION WAVE IN THREE DIMENSIONAL SPACE
	Wang, Guanfa 1; Wang, Yong 2,3; Zhou, Jiawei 4,5
刊名	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
	2021
卷号	53 期号:4 页码:4692-4726
关键词	Boltzmann equation compressible Euler equations hydrodynamic limit Hilbert expansion a priori estimate planar rarefaction wave
ISSN号	0036-1410
DOI	10.1137/20M1362905
英文摘要	In this paper, we establish the global-in-time hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave of a compressible Euler system in three dimensional space x is an element of R-3 for general collision kernels. Our approach is based on the Hilbert expansion and a recent L-2-L-infinity framework. In particular, we improve the L-2-estimate to be a localized version because the planar rarefaction wave is indeed a one dimensional wave which makes the source terms not integrable in the L-2 energy estimate of the three dimensional problem. We also point out that the wave strength of rarefaction may be large.
资助项目	National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11771429] ; National Natural Science Foundation of China[12022114] ; Youth Innovation Promotion Association of Chinese Academy of Sciences[2019002]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000692288300033
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59269]
专题	应用数学研究所
通讯作者	Wang, Guanfa
作者单位	1.South China Normal Univ, Zhong Shan Ave West 55, Guangzhou 510631, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 4.Wuhan Univ, Sch Math & Stat, Wuhan 100049, Peoples R China 5.Wuhan Univ, Comp Sci Hubei Key Lab, Wuhan 430072, Peoples R China
推荐引用方式 GB/T 7714	Wang, Guanfa,Wang, Yong,Zhou, Jiawei. HYDRODYNAMIC LIMIT OF THE BOLTZMANN EQUATION TO THE PLANAR RAREFACTION WAVE IN THREE DIMENSIONAL SPACE[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2021,53(4):4692-4726.
APA	Wang, Guanfa,Wang, Yong,&Zhou, Jiawei.(2021).HYDRODYNAMIC LIMIT OF THE BOLTZMANN EQUATION TO THE PLANAR RAREFACTION WAVE IN THREE DIMENSIONAL SPACE.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,53(4),4692-4726.
MLA	Wang, Guanfa,et al."HYDRODYNAMIC LIMIT OF THE BOLTZMANN EQUATION TO THE PLANAR RAREFACTION WAVE IN THREE DIMENSIONAL SPACE".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 53.4(2021):4692-4726.