GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM*

doi:10.1007/s10473-023-0113-8

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 205-236.doi: 10.1007/s10473-023-0113-8

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

Mingying zhong

College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China

收稿日期:2021-06-18 修回日期:2022-06-28 发布日期:2023-03-01
基金资助:
*National Natural Science Foun-dation of China (11671100 and 12171104), the National Science Fund for Excellent Young Scholars (11922107), and Guangxi Natural Science Foundation (2018GXNSFAA138210 and 2019JJG110010).

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

Mingying zhong

College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China

Received:2021-06-18 Revised:2022-06-28 Published:2023-03-01
About author:Mingying zhong,E-mail: zhongmingying@sina.com
Supported by:
*National Natural Science Foun-dation of China (11671100 and 12171104), the National Science Fund for Excellent Young Scholars (11922107), and Guangxi Natural Science Foundation (2018GXNSFAA138210 and 2019JJG110010).

摘要/Abstract

摘要： The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three dimensional space are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.

关键词: Vlasov-Poisson-Fokker-Planck system, Green's function, pointwise behavior, spectrum structure

Abstract: The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three dimensional space are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.

Key words: Vlasov-Poisson-Fokker-Planck system, Green's function, pointwise behavior, spectrum structure

Mingying zhong. GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*[J]. 数学物理学报(英文版), 2023, 43(1): 205-236.

Mingying zhong. GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 205-236.

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GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

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