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Related papers: Vlasov-Maxwell-Boltzmann diffusive limit

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In this work, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$. We establish the global existence, uniqueness and large time…

Analysis of PDEs · Mathematics 2024-05-29 Chuqi Cao , Dingqun Deng , Xingyu Li

We consider the compressible Vlasov-Poisson-Fokker-Planck-Navier-Stokes system in a three dimensional bounded domain with nonhomogeneous Dirichlet boundary conditions. The system describes the evolution of charged particles ensemble…

Analysis of PDEs · Mathematics 2023-01-04 Li Chen , Fucai Li , Yue Li , Nicola Zamponi

We construct a time-asymptotic expansion with pointwise remainder estimates for solutions to 1D compressible Navier--Stokes equations. The leading-order term is the well-known diffusion wave and the higher-order terms are newly introduced…

Analysis of PDEs · Mathematics 2023-09-12 Kai Koike

This paper concerns the diffusive limit of the time evolutionary Boltzmann equation in the half space $\mathbb{T}^2\times\mathbb{R}^+$ for a small Knudsen number $\varepsilon>0$. For boundary conditions in the normal direction, it involves…

Analysis of PDEs · Mathematics 2026-03-31 Hongxu Chen , Renjun Duan

We treat hydrodynamic limits of the Vlasov-Maxwell-Boltzmann system for one and two species of particles in a viscous incompressible regime.

Analysis of PDEs · Mathematics 2016-04-07 Diogo Arsénio , Laure Saint-Raymond

In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate…

Analysis of PDEs · Mathematics 2022-08-09 Mingying Zhong

Since the work [13] by Guo [Invent. Math. 153 (2003), no. 3, 593--630], how to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov-Maxwell-Boltzmann system with the whole range of soft…

Analysis of PDEs · Mathematics 2014-11-20 Renjun Duan , Yuanjie Lei , Tong Yang , Huijiang Zhao

We consider a self-gravitating collisionless gas as described by the Vlasov-Poisson or Einstein-Vlasov system or a self-gravitating fluid ball as described by the Euler-Poisson or Einstein-Euler system. We give a simple proof for the finite…

General Relativity and Quantum Cosmology · Physics 2013-12-16 Tobias Ramming , Gerhard Rein

In this paper, we study the hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for a gas mixture in the whole space $(x \in \mathbb{R}^3)$ with the potential range of $\gamma \in\left(-3, 1\right]$. Using the method of Hilbert…

Analysis of PDEs · Mathematics 2026-01-30 Yeping Li , Gaofeng Wang , Tianfang Wu

Strict mathematics reveals that the strict solution of a Vlasov-Maxwell equation set cannot be of a zero-temperature mathematical form. This universal property of Vlasov-Maxwell system can lead to a closed equation set of three macroscopic…

Plasma Physics · Physics 2014-03-03 H. Lin

In the diffusive scaling and in the whole space, we prove the global well-posedness of the scaled Boltzmann-Bose-Einstein (briefly, BBE) equation with high temperature in the low regularity space $H^2_xL^2$. In particular, we quantify the…

Analysis of PDEs · Mathematics 2023-08-23 Ling-Bing He , Ning Jiang , Yu-long Zhou

The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure…

Analysis of PDEs · Mathematics 2024-06-19 Miroslav Buliček , Ansgar Jüngel , Milan Pokorný , Nicola Zamponi

We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop…

Analysis of PDEs · Mathematics 2025-10-07 Yuanjie Lei , Shuangqian Liu , Qinghua Xiao , Huijiang Zhao

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator.…

Analysis of PDEs · Mathematics 2017-10-25 Renjun Duan , Shuangqian Liu

The large-time asymptotics of weak solutions to Maxwell--Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither…

Analysis of PDEs · Mathematics 2019-07-29 Esther S. Daus , Ansgar Jüngel , Bao Quoc Tang

We establish the exponential time decay rate of smooth solutions of small amplitude to the Vlasov-Poisson-Fokker-Planck equations to the Maxwellian both in the whole space and in the periodic box via the uniform-in-time energy estimates and…

Analysis of PDEs · Mathematics 2011-12-26 Hyung Ju Hwang , Juhi Jang

For the one-species Vlasov-Poisson-Boltzmann (VPB) system in the scaling under which the moments of the fluctuations formally converge to the incompressible Navier-Stokes-Fourier-Poisson (NSFP) system, we prove the uniform estimates with…

Analysis of PDEs · Mathematics 2020-07-02 Mengmeng Guo , Ning Jiang , Yi-Long Luo

We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…

Analysis of PDEs · Mathematics 2015-06-16 Ricardo J. Alonso , Bertrand Lods

The global well-posedness and inviscid limit are investigated for the fluid-particle interaction system, described by the Navier-Stokes equations for the inhomogeneous incompressible viscous flows coupled with the Vlasov-Fokker-Planck…

Analysis of PDEs · Mathematics 2025-12-15 Fucai Li , Jinkai Ni , Ling-Yun Shou , Dehua Wang

We study well-posedness and long time behavior of the nonlinear Vlasov-Poisson- Fokker-Planck system with an external confining potential. The system describes the time evolution of particles (e.g.$\,\,$in a plasma) undergoing diffusion,…

Analysis of PDEs · Mathematics 2024-06-24 Gayrat Toshpulatov