Related papers: Vlasov-Maxwell-Boltzmann diffusive limit
In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…
When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…
The exterior domain problem is essential in fluid and kinetic equations. In this paper, we establish the validity of the diffusive expansion for the Boltzmann equations to the Navier-Stokes-Fourier system up to the critical time in an…
This paper is devoted to the study of the dynamics of charged particles in a weakly inhomogeneous dilute gas. More precisely, we consider the existence of unique global in time classical solutions for the Vlasov-MaxwellBoltzmann system and…
We provide a quantitative asymptotic analysis for the nonlinear Vlasov--Poisson--Fokker--Planck system with a large linear friction force and high force-fields. The limiting system is a diffusive model with nonlocal velocity fields often…
In this paper, we are interested in the dynamics of charged particles interacting with the incompressible viscous flow. More precisely, we consider the Vlasov-Poisson or Vlasov-Poisson-Fokker-Planck equation coupled with the incompressible…
In this paper, we study the Vlasov-Maxwell-Boltzmann system without angular cutoff and the Vlasov-Maxwell-Landau/Boltzmann system with polynomial perturbation $F=\mu+f$ near global Maxwellian. In particular, we prove the global existence,…
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that…
Recently, the authors proved [2] that the Maxwell-Stefan system with an incompressibility-like condition on the total flux can be rigorously derived from the multi-species Boltzmann equation. Similar cross-diffusion models have been widely…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
The study of flows over an obstacle is one of the fundamental problems in fluids. In this paper we establish the global validity of the diffusive limit for the Boltzmann equations to the Navier-Stokes-Fourier system in an exterior domain.…
For the two-species Vlasov-Maxwell-Boltzmann (VMB) system with the scaling under which the moments of the fluctuations to the global Maxwellians formally converge to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) system…
The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture…
We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional…
Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and…
By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown that the electric…
This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck model. We derive a priori estimates which hold without restriction on the phase-space dimension and propose a strong convergence result in a L2 space. Furthermore,…
It is well known that the full compressible Navier-Stokes equations can be deduced via the Chapman-Enskog expansion from the Boltzmann equation as the first-order correction to the Euler equations with viscosity and heat-conductivity…
We derive the incompressible Euler equations with heat convection with the no-penetration boundary condition from the Boltzmann equation with the diffuse boundary in the hydrodynamic limit for the scale of large Reynold number. Inspired by…
The present contribution investigates the dynamics generated by the two-dimensional Vlasov-Poisson-Fokker-Planck equation for charged particles in a steady inhomogeneous background of opposite charges. We provide global in time estimates…