THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

doi:10.1016/S0252-9602(16)30057-1

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (4): 1049-1097.doi: 10.1016/S0252-9602(16)30057-1

THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

王路生^1,2, 肖清华³, 熊林杰⁴, 赵会江^1,5

1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2 Department of Mathematics, Northwest University, Xi'an 710127, China;
3 Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
4 College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;
5 Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China

收稿日期:2015-05-18 修回日期:2016-01-25 出版日期:2016-08-25 发布日期:2016-08-25
通讯作者: Huijiang ZHAO,E-mail:hhjjzhao@hotmail.com E-mail:hhjjzhao@hotmail.com
作者简介:Lusheng WANG,E-mail:mathwls08@gmail.com;Qinghua XIAO,E-mail:pdexqh@hotmail.com;Linjie XIONG,E-mail:xlj@hnu.edu.cn
基金资助:
The work of Lusheng Wang was supported by the Fundamental Research Funds for the Central Universities, the work of Qinghua Xiao was supported by a grant from the National Science Foundation of China under contract 11501556, the work of Linjie Xiong was supported by a grant from the National Natural Science Foundation under contract 11501187, and the work of Huijiang Zhao was supported by three grants from the National Natural Science Foundation of China under contracts 10925103, 11271160, and 11261160485, respectively.

THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

Lusheng WANG^1,2, Qinghua XIAO³, Linjie XIONG⁴, Huijiang ZHAO^1,5

1 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
2 Department of Mathematics, Northwest University, Xi'an 710127, China;
3 Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China;
4 College of Mathematics and Econometrics, Hunan University, Changsha 410082, China;
5 Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China

Received:2015-05-18 Revised:2016-01-25 Online:2016-08-25 Published:2016-08-25
Contact: Huijiang ZHAO,E-mail:hhjjzhao@hotmail.com E-mail:hhjjzhao@hotmail.com
Supported by:
The work of Lusheng Wang was supported by the Fundamental Research Funds for the Central Universities, the work of Qinghua Xiao was supported by a grant from the National Science Foundation of China under contract 11501556, the work of Linjie Xiong was supported by a grant from the National Natural Science Foundation under contract 11501187, and the work of Huijiang Zhao was supported by three grants from the National Natural Science Foundation of China under contracts 10925103, 11271160, and 11261160485, respectively.

摘要/Abstract

摘要：

In this article, we are concerned with the construction of global smooth smallamplitude solutions to the Cauchy problem of the one species Vlasov-Poisson-Boltzmann system near Maxwellians for long-range interactions. Compared with the former result obtained by Duan and Liu in[12] for the two species model, we do not ask the initial perturbation to satisfy the neutral condition and our result covers all physical collision kernels for the full range of intermolecular repulsive potentials.

关键词: One-species Vlasov-Poisson-Boltzmann system, long-range interactions, global solutions near Maxwellians, time-velocity weighted energy method

Abstract:

Key words: One-species Vlasov-Poisson-Boltzmann system, long-range interactions, global solutions near Maxwellians, time-velocity weighted energy method

中图分类号:

35Q20

王路生, 肖清华, 熊林杰, 赵会江. THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS[J]. 数学物理学报(英文版), 2016, 36(4): 1049-1097.

Lusheng WANG, Qinghua XIAO, Linjie XIONG, Huijiang ZHAO. THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS[J]. Acta mathematica scientia,Series B, 2016, 36(4): 1049-1097.

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THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

THE VLASOV-POISSON-BOLTZMANN SYSTEM NEAR MAXWELLIANS FOR LONG-RANGE INTERACTIONS

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