STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

doi:10.1007/s10473-019-0112-y

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 127-138.doi: 10.1007/s10473-019-0112-y

STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

廖杰¹, 王倩蓉¹, 杨雄锋²

1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
2. School of Mathematical Sciences;Key Laboratory of Scientific and Engineering Computing(MOE), Shanghai Jiao Tong University, Shanghai, 200240, China

收稿日期:2017-09-15 修回日期:2018-02-24 出版日期:2019-02-25 发布日期:2019-03-13
通讯作者: Jie LIAO E-mail:liaojie@ecust.edu.cn
作者简介:Qianrong WANG,475446014@qq.com;Xiongfeng YANG,xf-yang@sjtu.edu.cn
基金资助:
The research was partially supported by Fundamental Research Funds for the Central Universities, NSFC (11871335) and by the SJTU's SMC Projection.

STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

Jie LIAO¹, Qianrong WANG¹, Xiongfeng YANG²

1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China;
2. School of Mathematical Sciences;Key Laboratory of Scientific and Engineering Computing(MOE), Shanghai Jiao Tong University, Shanghai, 200240, China

Received:2017-09-15 Revised:2018-02-24 Online:2019-02-25 Published:2019-03-13
Contact: Jie LIAO E-mail:liaojie@ecust.edu.cn
Supported by:
The research was partially supported by Fundamental Research Funds for the Central Universities, NSFC (11871335) and by the SJTU's SMC Projection.

摘要/Abstract

摘要： In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov—Poisson—Fokker—Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker—Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker—Planck operator.

关键词: non-linear Vlasov-Poisson-Fokker-Planck equation, global Maxwellian, global a priori estimates, exponential convergence

Abstract: In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov—Poisson—Fokker—Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker—Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker—Planck operator.

Key words: non-linear Vlasov-Poisson-Fokker-Planck equation, global Maxwellian, global a priori estimates, exponential convergence

廖杰, 王倩蓉, 杨雄锋. STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(1): 127-138.

Jie LIAO, Qianrong WANG, Xiongfeng YANG. STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS[J]. Acta mathematica scientia,Series B, 2019, 39(1): 127-138.

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STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

STABILITY OF GLOBAL MAXWELLIAN FOR NON-LINEAR VLASOV-POISSON-FOKKER-PLANCK EQUATIONS

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