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The motion of a collisionless plasma is described by the Vlasov-Poisson system, or in the presence of large velocities, the relativistic Vlasov-Poisson system. Both systems are considered in one space and one momentum dimension, with two…

Analysis of PDEs · Mathematics 2010-03-01 Stephen Pankavich , Robert Glassey , Jack Schaeffer

This paper reviews results on the scalar Boltzmann equation for a single-component polyatomic gas with continuous internal energy. For the space homogeneous problem, $L^1$-theory is established, for solutions with initial strictly positive…

Analysis of PDEs · Mathematics 2025-02-28 Ricardo Alonso , Milana Colic

In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or finite channel. The main goal is to establish the global existence and large time behavior…

Analysis of PDEs · Mathematics 2024-02-08 Dingqun Deng , Renjun Duan

This paper presents a grid-free simulation algorithm for the fully three-dimensional Vlasov--Poisson system for collisionless electron plasmas. We employ a standard particle method for the numerical approximation of the distribution…

Numerical Analysis · Mathematics 2020-03-06 Torsten Keßler , Sergej Rjasanow , Steffen Weißer

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

We prove the unique existence and exponential decay of global in time classical solutions to the special relativistic Boltzmann equation without any angular cut-off assumptions with initial perturbations in some weighted Sobolev spaces. We…

Analysis of PDEs · Mathematics 2021-02-19 Jin Woo Jang

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the…

Analysis of PDEs · Mathematics 2015-05-14 Stephen Pankavich

Based on the recent study on the Vlasov-Poisson-Boltzmann system with general angular cutoff potentials [3, 4], we establish in this paper the global existence of classical solutions to the Cauchy problem of the Vlasov-Poisson-Landau system…

Analysis of PDEs · Mathematics 2011-12-15 Renjun Duan , Tong Yang , Huijiang Zhao

In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous…

Analysis of PDEs · Mathematics 2015-05-18 Carlo Marchioro , Evelyne Miot , Mario Pulvirenti

The time evolution of a two-component collisionless plasma is modeled by the Vlasov-Poisson system. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of…

Mathematical Physics · Physics 2021-12-01 Patrik Knopf , Jörg Weber

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

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 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

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

A collisionless plasma is modeled by the Vlasov-Poisson system in one-dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge…

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

The Boltzmann equation without an angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian with an algebraic decay in the velocity variable. A well-posedness theory in the perturbative framework is…

Analysis of PDEs · Mathematics 2019-01-08 Ricardo Alonso , Yoshinori Morimoto , Weiran Sun , Tong Yang

While a fully relativistic collisionless plasma is modeled by the Vlasov-Maxwell system a good approximation in the non-relativistic limit is given by the Vlasov-Poisson system. We modify the Vlasov-Poisson system so that damping due to the…

Mathematical Physics · Physics 2016-04-21 Sebastian Bauer

The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the…

Analysis of PDEs · Mathematics 2015-12-03 Yoshinori Morimoto , Shota Sakamoto

The boundary problem about behavior (oscillations) of the electronic plasmas with arbitrary degree of degeneration of electronic gas in half-space with specular boundary conditions is analytically solved. The kinetic equation of…

Plasma Physics · Physics 2017-03-07 A. V. Latyshev , S. Sh. Suleymanova

We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…

Numerical Analysis · Mathematics 2025-10-20 Gerhard Rein , Thomas Rodewis