Vlasov-Poisson-Boltzmann 方程组的 Navier-Stokes-Poisson 方程组逼近——献给陈化教授 70 寿辰

数学物理学报 ›› 2026, Vol. 46 ›› Issue (2): 683-708.

Vlasov-Poisson-Boltzmann 方程组的 Navier-Stokes-Poisson 方程组逼近——献给陈化教授 70 寿辰

董丽娜(), 刘双乾(), 马璇(), 马袁园^*()

华中师范大学数学与统计学学院武汉 430079

收稿日期:2025-12-31 修回日期:2026-01-27 出版日期:2026-04-26 发布日期:2026-04-27
通讯作者: 马袁园 E-mail:2163835253@mails.ccnu.edu.cn;sqliu@ccnu.edu.cn;maxuan@ccnu.edu.cn;yyma@mails.ccnu.edu.cn
作者简介:董丽娜, Email：2163835253@mails.ccnu.edu.cn
刘双乾, Email：sqliu@ccnu.edu.cn
马璇, Email：maxuan@ccnu.edu.cn
基金资助:
国家自然科学基金(12325107)

Compressible Navier-Stokes-Poisson System Approximation to the Vlasov-Poisson-Boltzmann System

Lina Dong(), Shuangqian Liu(), Xuan Ma(), Yuanyuan Ma^*()

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079

Received:2025-12-31 Revised:2026-01-27 Online:2026-04-26 Published:2026-04-27
Contact: Yuanyuan Ma E-mail:2163835253@mails.ccnu.edu.cn;sqliu@ccnu.edu.cn;maxuan@ccnu.edu.cn;yyma@mails.ccnu.edu.cn
Supported by:
NSFC(12325107)

摘要/Abstract

摘要：

当 Knudsen 数趋于 $0$ 时, 可压缩 Navier-Stokes-Poisson 方程组并不是无量纲化 Vlasov-Poisson-Boltzmann 方程组的极限, 但通过 Chapman-Enskog 展开, 它是 Vlasov-Poisson-Boltz-mann 方程组的二阶近似. 该文的目的是严格证明若可压缩 Navier-Stokes-Poisson 方程组对应的局部 Maxwellian 与 Vlasov-Poisson-Boltzmann 方程组的初值之差是 Knudsen 数的二阶小量, 则两者解在所有时间内的差也保持该量级. 该文的分析基于宏观方程的能量估计以及宏观-微观分解框架下的精细能量方法.

关键词: Vlasov-Poisson-Boltzmann 方程组, 宏观-微观分解, 可压缩 Navier-Stokes-Poisson 方程组

Abstract:

When the Knudsen number approaches zero, the compressible Navier-Stokes-Poisson (NSP) system is not the limit of the dimensionless Vlasov-Poisson-Boltzmann (VPB) system; however, via the Chapman-Enskog expansion, it constitutes a second-order approximation to the VPB system. The purpose of this paper is to rigorously prove that if the difference between the local Maxwellian corresponding to the compressible NSP system and the initial value of the VPB system is a second-order small quantity in the Knudsen number, then the solutions of the two systems will maintain this order of magnitude difference for all times. The analysis in this paper is based on the energy estimates of the macroscopic equations, as well as the refined energy method within the macroscopic-microscopic decomposition framework.

Key words: Vlasov-Poisson-Boltzmann system, macroscopic-microscopic decomposition, compressible Navier-Stokes-Poisson system

中图分类号:

O175.2

董丽娜, 刘双乾, 马璇, 马袁园. Vlasov-Poisson-Boltzmann 方程组的 Navier-Stokes-Poisson 方程组逼近——献给陈化教授 70 寿辰[J]. 数学物理学报, 2026, 46(2): 683-708.

Lina Dong, Shuangqian Liu, Xuan Ma, Yuanyuan Ma. Compressible Navier-Stokes-Poisson System Approximation to the Vlasov-Poisson-Boltzmann System[J]. Acta mathematica scientia,Series A, 2026, 46(2): 683-708.

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