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The ionic Vlasov-Poisson-Boltzmann system is a fundamental model in dilute collisional plasmas. In this work, we study the compressible ionic Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for the full range of cutoff…

Analysis of PDEs · Mathematics 2026-01-14 Qin Ye , Fujun Zhou , Weijun Wu

The Vlasov-Maxwell-Landau (VML) system and the Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the hydrodynamic limits of both the VML and the non-cutoff VMB…

Analysis of PDEs · Mathematics 2023-11-28 Yuanjie Lei , Shuangqian Liu , Qinghua Xiao , Huijiang Zhao

We study the Hilbert expansion for small Knudsen number $\varepsilon$ for the Vlasov-Boltzmann-Poisson system for an electron gas. The zeroth order term takes the form of local Maxwellian: $ F_{0}(t,x,v)=\frac{\rho_{0}(t,x)}{(2\pi…

Analysis of PDEs · Mathematics 2015-05-14 Yan Guo , Juhi Jang

Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and…

Analysis of PDEs · Mathematics 2023-01-11 Yan Guo , Qinghua Xiao

In this paper, we study the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is to give a rigorous derivation of the compressible Euler…

Analysis of PDEs · Mathematics 2022-10-03 Yuanjie Lei , Shuangqian Liu , Qinghua Xiao , Huijiang Zhao

In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…

Analysis of PDEs · Mathematics 2026-05-19 Yong Wang , Hang Xiong , Hongyao Zhang

In the present paper, we concern the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition in a two-dimensional disk to the compressible Euler equations. Due to the non-zero curvature and non-zero tangential…

Analysis of PDEs · Mathematics 2025-04-22 Feimin Huang , Jing Ouyang , Yong Wang

Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…

Analysis of PDEs · Mathematics 2023-06-02 Renjun Duan , Dongcheng Yang , Hongjun Yu

We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional…

Analysis of PDEs · Mathematics 2025-12-04 Fucai Li , Yichun Wang

Boundary effects play an important role in the study of hydrodynamic limits in the Boltzmann theory. We justify rigorously the validity of the hydrodynamic limit from the Boltzmann equation of soft potentials to the compressible Euler…

Analysis of PDEs · Mathematics 2023-10-05 Jing Ouyang , Yong Wang

A fundamental two-fluid model for describing dynamics of a plasma is the Euler-Poisson system, in which compressible ion and electron fluids interact with their self-consistent electrostatic force. Global smooth electron dynamics were…

Mathematical Physics · Physics 2015-05-18 Yan Guo , Benoit Pausader

Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff in the framework of perturbation around global Maxwellian still remains open. By employing the weighted energy method with a newly introduced weight function…

Analysis of PDEs · Mathematics 2024-05-16 Yuan Xu , Fujun Zhou , Yongsheng Li

An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…

Analysis of PDEs · Mathematics 2012-03-20 Renjun Duan , Tong Yang , Huijiang Zhao

The study of hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to appearance of the viscous and Knudsen boundary layers. In this paper, the hydrodynamic limit from the Boltzmann equation with…

Analysis of PDEs · Mathematics 2023-09-11 Feimin Huang , Weiqiang Wang , Yong Wang , Feng Xiao

In the paper, we consider the Cauchy problem on the spatially one-dimensional Vlasov-Poisson-Landau system modelling the motion of ions under a generalized Boltzmann relation. Let the Knudsen number and the Debye length be given as…

Analysis of PDEs · Mathematics 2022-12-16 Renjun Duan , Dongcheng Yang , Hongjun Yu

Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible 3-D Euler-Poisson system without any symmetry assumptions in both the…

Analysis of PDEs · Mathematics 2017-12-04 Mahir Hadzic , Juhi Jang

We study the derivation of ion dynamics, namely, the ionic Euler--Poisson system, from kinetic descriptions. The kinetic framework consists of the ionic Vlasov--Poisson equation coupled with either a nonlinear Fokker--Planck operator or a…

Analysis of PDEs · Mathematics 2025-08-13 Young-Pil Choi , Dowan Koo , Sihyun Song

The relativistic Vlasov-Maxwell-Landau (r-VML) system and the relativistic Landau equation (r-LAN) are fundamental models that describe the dynamics of an electron gas. In this paper, we introduce a novel weighted energy method and…

Analysis of PDEs · Mathematics 2023-06-08 Zhimeng Ouyang , Lei Wu , Qinghua Xiao

Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where…

Analysis of PDEs · Mathematics 2021-05-27 Megan Griffin-Pickering , Mikaela Iacobelli

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. By using the dispersive Klein-Gordon effect, Guo \cite{Guo98} first…

Analysis of PDEs · Mathematics 2011-09-21 Juhi Jang , Dong Li , Xiaoyi Zhang
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