Related papers: Diffusive Limit of the Vlasov-Maxwell-Boltzmann Sy…
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…
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…
In this paper, we study the hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for a gas mixture in the whole space $(x \in \mathbb{R}^3)$ with the potential range of $\gamma \in\left(-3, 1\right]$. Using the method of Hilbert…
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…
In this work, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$. We establish the global existence, uniqueness and large time…
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 initial-boundary value problem for the inhomogeneous non-cutoff Boltzmann equation is a challenging open problem. In this paper, we study the stability and long-time dynamics of the Boltzmann equation near a global Maxwellian without…
While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017],…
Since the work [13] by Guo [Invent. Math. 153 (2003), no. 3, 593--630], how to establish the global existence of perturbative classical solutions around a global Maxwellian to the Vlasov-Maxwell-Boltzmann system with the whole range of soft…
We study the diffusion limit of the strong solution to the Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. By introducing a new decomposition of the solution to identify the essential components for…
The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods,…
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.…
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…
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…
In the present paper, we study the diffusion limit of the strong solution to the one-species Vlasov-Maxwell-Boltzmann (VMB) system with initial data near a global Maxwellian. Based on spectral analysis techniques, we prove the convergence…
The hydrodynamic limit of the Vlasov-Maxwell-Boltzmann equations is considered for weak solutions. Using relative entropy estimate about an absolute Maxwellian, an incompressible Electron-Magnetohydrodynamics-Fourier limit for solutions of…
This is the first one of two papers on the global dynamics of the original Boltzmann equations without angular cutoff on the torus. We address the problem for the hard potentials and Maxwellian molecules in the present paper. The case of…
In the present paper, we study the diffusion limit of the classical solution to the modified Vlasov-Poisson-Boltzmann (mVPB) System with initial data near a global Maxwellian. Based on the spectral analysis, weprove the convergence and…
We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…
We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…