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In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions…

Analysis of PDEs · Mathematics 2021-09-22 Dingqun Deng

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

This work concerns the Vlasov-Poisson-Boltzmann system without angular cutoff and Vlasov-Poisson-Landau system including Coulomb interaction in bounded domain, namely union of cubes. We establish the global stability, exponential large-time…

Analysis of PDEs · Mathematics 2022-08-24 Dingqun Deng

We consider the non-cutoff Vlasov-Poisson-Boltzmann (VPB) system of two species with soft potential in the whole space $\mathbb{R}^3$ when an initial data is near Maxwellian. Continuing the work Deng [Comm. Math. Phys. 387, 1603-1654…

Analysis of PDEs · Mathematics 2024-02-08 Dingqun Deng

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

It is known that in the parameters range $-2 \leq \gamma <-2s$ spectral gap does not exist for the linearized Boltzmann operator without cutoff but it does for the linearized Landau operator. This paper is devoted to the understanding of…

Analysis of PDEs · Mathematics 2021-05-31 Duan Renjun , He Ling-Bing , Yang Tong , Yu-Long Zhou

Motivated by the fundamental model of a collisionless plasma, the Vlasov-Maxwell (VM) system, we consider a related, nonlinear system of partial differential equations in one space and one momentum dimension. As little is known regarding…

Analysis of PDEs · Mathematics 2015-09-01 Charles Nguyen , Jennifer Anderson , Stephen Pankavich

Diffusive limit of the non-cutoff Vlasov-Maxwell-Boltzmann system in perturbation framework still remains open. By employing a new weight function and making full use of the anisotropic dissipation property of the non-cutoff linearized…

Analysis of PDEs · Mathematics 2024-05-20 Yuan Xu , Fujun Zhou , Weihua Gong , Weijun Wu

This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials, $r^{-(p-1)}$ with $p>2$, for initial…

Analysis of PDEs · Mathematics 2011-04-05 Philip T. Gressman , Robert M. Strain

In this paper, we are concerned with the Vlasov-Poisson-Boltzmann (VPB) system in three-dimensional spatial space without angular cutoff in a rectangular duct with or without physical boundary conditions. Near a local Maxwellian with…

Analysis of PDEs · Mathematics 2022-12-13 Dingqun Deng

We construct a unique global-in-time solution to the two species Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition, which can be viewed as one of the ideal scattering boundary model. The construction…

Analysis of PDEs · Mathematics 2019-06-07 Yunbai Cao

The Vlasov-Maxwell-Boltzmann system is a fundamental model to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of…

Analysis of PDEs · Mathematics 2010-05-02 Robert M. Strain

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

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

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 motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…

Analysis of PDEs · Mathematics 2016-04-18 Robert Glassey , Stephen Pankavich , Jack Schaeffer

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

A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge - dependant upon only velocity - is assumed. The situation in which mobile negative ions balance the positive…

Analysis of PDEs · Mathematics 2010-01-06 Stephen Pankavich

This paper is concerned with the relativistic Boltzmann equation without angular cutoff. We establish the global-in-time existence, uniqueness, and asymptotic stability for solutions nearby the relativistic Maxwellian. We work in the case…

Analysis of PDEs · Mathematics 2022-07-08 Jin Woo Jang , Robert M. Strain

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle…

Analysis of PDEs · Mathematics 2009-12-31 Robert Glassey , Stephen Pankavich , Jack Schaeffer
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