REGULARITY OF SOLUTIONS FOR SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF

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	REGULARITY OF SOLUTIONS FOR SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF
	Huo, Zhaohui 1,2; Morimoto, Yoshinori 3; Ukai, Seiji 4; Yang, Tong 1,5
	2008-09-01
发表期刊	KINETIC AND RELATED MODELS
ISSN	1937-5093
卷号	1 期号:3 页码:453-489
摘要	The spatially homogeneous Boltzmann equation without angular cutoff is discussed on the regularity of solutions for the modified hard potential and Debye-Yukawa potential. When the angular singularity of the cross section is moderate, any weak solution having the finite mass, energy and entropy lies in the Sobolev space of infinite order for any positive time, while for the general potentials, it lies in the Schwartz space if it has moments of arbitrary order. The main ingredients of the proof are the suitable choice of the mollifiers composed of pseudo-differential operators and the sharp estimates of the commutators of the Boltzmann collision operator and pseudo-differential operators. The method developed here also provides some new estimates on the collision operator.
关键词	Boltzmann equation angular non-cutoff regularity pseudo-differential operators commutator
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000268957600008
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6180
专题	中国科学院数学与系统科学研究院
通讯作者	Huo, Zhaohui
作者单位	1.City Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China 2.Acad Math & Syst Sci, CAS, Inst Math, Beijing 100190, Peoples R China 3.Kyoto Univ, Grad Sch Human & Environm Studies, Kyoto 6068501, Japan 4.City Univ Hong Kong, Lie Bie Ju Ctr Math Sci, Hong Kong, Hong Kong, Peoples R China 5.Shanghai Jiao Tong Univ, Dept Math, Shanghai 200030, Peoples R China
推荐引用方式 GB/T 7714	Huo, Zhaohui,Morimoto, Yoshinori,Ukai, Seiji,et al. REGULARITY OF SOLUTIONS FOR SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF[J]. KINETIC AND RELATED MODELS,2008,1(3):453-489.
APA	Huo, Zhaohui,Morimoto, Yoshinori,Ukai, Seiji,&Yang, Tong.(2008).REGULARITY OF SOLUTIONS FOR SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF.KINETIC AND RELATED MODELS,1(3),453-489.
MLA	Huo, Zhaohui,et al."REGULARITY OF SOLUTIONS FOR SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF".KINETIC AND RELATED MODELS 1.3(2008):453-489.