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This paper considers a system of Boltzmann equations modelling the mixture of monatomic and polyatomic gases in an $L^{2}-L^{\infty}$ perturbation theory around global modified Maxwellians accounting for the internal energy of the mixture…

Analysis of PDEs · Mathematics 2025-11-20 Ricardo Alonso , Zongguang Li

When particle speeds are large the motion of a collisionless plasma is modeled by the relativistic Vlasov Maxwell system. Large time behavior of solutions which depend on one position variable and two momentum variables is considered. In…

Analysis of PDEs · Mathematics 2010-01-02 Robert Glassey , Stephen Pankavich , Jack Schaeffer

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

Analysis of PDEs · Mathematics 2021-06-09 Hai-Liang Li , Tong Yang , Mingying Zhong

In a recent paper Calogero and Alcantara derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half"…

Analysis of PDEs · Mathematics 2015-09-01 Stephen Pankavich , Nicholas Michalowski

Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we…

Analysis of PDEs · Mathematics 2010-11-19 Emmanuel Frénod , Eric Sonnendrücker

This paper proves existence of a global weak solution to the inhomogeneous (i.e., non-constant density) incompressible Navier-Stokes system with mass diffusion. The system is well-known as the Kazhikhov-Smagulov model. The major novelty of…

Analysis of PDEs · Mathematics 2023-06-19 Eliott Kacedan , Kohei Soga

In this Letter, weak turbulence theory is used to investigate interactions among Alfven waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of…

Astrophysics · Physics 2009-11-13 Benjamin D. G. Chandran

A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a…

Analysis of PDEs · Mathematics 2022-05-16 Xiaokai Huo , Ansgar Jüngel , Athanasios E. Tzavaras

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…

Statistical Mechanics · Physics 2014-10-07 Avik Biswas , A. Bhattacharyay

We study the long-time behavior of radially symmetric solutions to the Vlasov-Poisson equation consisting of an attractive point mass and a small, suitably localized and absolutely continuous distribution of particles: if the latter is…

Analysis of PDEs · Mathematics 2025-11-07 Bernhard Kepka , Klaus Widmayer

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

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither…

Analysis of PDEs · Mathematics 2014-12-03 Miguel Escobedo , Minh-Binh Tran

We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\lambda$> 0, the one-particle distribution function has a…

Analysis of PDEs · Mathematics 2012-09-04 Reinel Sospedra-Alfonso

Numerical schemes that preserve the structure of the kinetic equations can provide stable simulation results over a long time. An electromagnetic particle-in-cell solver for the Vlasov-Maxwell equations that preserves at the discrete level…

Numerical Analysis · Mathematics 2020-02-24 Benedikt Perse , Katharina Kormann , Eric Sonnendrücker

This paper discusses energy-conserving time-discretizations for finite element particle-in-cell discretizations of the Vlasov--Maxwell system. A geometric spatially discrete system can be obtained using a standard particle-in-cell…

Numerical Analysis · Mathematics 2020-10-21 Katharina Kormann , Eric Sonnendrücker

We study the velocity distribution function for inelastic Maxwell models, characterized by a Boltzmann equation with constant collision rate, independent of the energy of the colliding particles. By means of a nonlinear analysis of the…

Statistical Mechanics · Physics 2009-11-07 Matthieu H. Ernst , Ricardo Brito

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 one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution…

Analysis of PDEs · Mathematics 2023-04-07 Hai-Liang Li , Ling-Yun Shou

The Vlasov-Poisson-Boltzmann System governs the time evolution of the distribution function for the dilute charged particles in the presence of a self-consistent electric potential force through the Poisson equation. In this paper, we are…

Analysis of PDEs · Mathematics 2011-04-05 Renjun Duan , Robert M. Strain

We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak…

Analysis of PDEs · Mathematics 2016-03-14 Stephan De Bièvre , Arthur Vavasseur , Thierry Goudon