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Related papers: Global strong solutions in $\mathbb{R}^3$ for ioni…

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The fundamental "two-fluid" model for describing plasma dynamics is given by the Euler-Maxwell system, in which compressible ion and electron fluids interact with their own self-consistent electromagnetic field. We prove global stability of…

Analysis of PDEs · Mathematics 2013-03-06 Yan Guo , Alexandru D. Ionescu , Benoit Pausader

A collisionless plasma is modeled by the Vlasov-Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as x tends to…

Analysis of PDEs · Mathematics 2010-03-01 Stephen Pankavich

For a class of arbitrary large initial data with radial symmetry or cylindrical symmetry, we prove the existence of global solutions for the $3D$ relativistic Vlasov-Poisson system for the plasma physics case. The compact support assumption…

Analysis of PDEs · Mathematics 2022-03-03 Xuecheng Wang

We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…

Analysis of PDEs · Mathematics 2016-08-16 José A. Carrillo , Simon Labrunie

We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…

Analysis of PDEs · Mathematics 2017-05-15 Yoshikazu Giga , Slim Ibrahim , Shengyi Shen , Tsuyoshi Yoneda

In this paper we prove global existence for solutions of the Vlasov-Poisson system in convex bounded domains with specular boundary conditions and with a prescribed outward electrical field at the boundary.

Analysis of PDEs · Mathematics 2015-05-13 Hyung Ju Hwang , Juan J. L. Velazquez

We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a…

In this paper we established the global well-posedness theorem for a special type of wave-Klein-Gordon system that have the strong coupling terms in divergence form on the right hand side of its wave equation. We cope with the problem by…

Analysis of PDEs · Mathematics 2020-10-20 Senhao Duan , Yue Ma

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

We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein--Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or…

Analysis of PDEs · Mathematics 2009-03-20 Uwe Brauer , Lavi Karp

We justify the global-in-time validity of Hilbert expansion for the ionic Vlasov-Poisson-Boltzmann system in $\mathbb{R}^3$, a fundamental model describing ion dynamics in dilute collisional plasmas. As the Knudsen number approaches zero,…

Analysis of PDEs · Mathematics 2026-01-06 Fucai Li , Yichun Wang

The Vlasov-Poisson system for ions is a kinetic equation for dilute, unmagnetised plasma. It describes the evolution of the ions in a plasma under the assumption that the electrons are thermalized. Consequently, the Poisson coupling for the…

Analysis of PDEs · Mathematics 2026-05-15 Megan Griffin-Pickering

We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small C^k norms for the charge…

Analysis of PDEs · Mathematics 2019-10-15 Katherine Zhiyuan Zhang

The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range…

Analysis of PDEs · Mathematics 2012-05-25 Renjun Duan

The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…

Analysis of PDEs · Mathematics 2015-06-19 Qinghua Xiao , Linjie Xiong , Huijiang Zhao

We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…

Analysis of PDEs · Mathematics 2015-11-03 Mihaï Bostan , Aurélie Finot , Maxime Hauray

We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two…

Analysis of PDEs · Mathematics 2022-12-27 Dapeng Du , Jingyu Li , Yansheng Ma , Ruyi Pang

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

Analysis of PDEs · Mathematics 2023-08-21 Renjun Duan , Dongcheng Yang , Hongjun Yu

We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property.…

Analysis of PDEs · Mathematics 2017-08-09 Jonathan Ben-Artzi , Simone Calogero , Stephen Pankavich

The Vlasov-Poisson system is a classical model in physics used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions $d\leq 3$ under…

Analysis of PDEs · Mathematics 2018-02-21 Luigi Ambrosio , Maria Colombo , Alessio Figalli