Yunbai Cao, Chanwoo Kim
We discuss some recent development on the Vlasov-Poisson-Boltzmann system in bounded domains with diffuse reflection boundary condition. In addition we present a new regularity result when the particles are surrounded by conductor boundary.
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For the whole range of cutoff intermolecular interactions, we give a rigorous mathematical justification of the limit from the Vlasov-Maxwell-Boltzmann system to the Vlasov-Poisson-Boltzmann system as the light speed tends to infinity.Such a limit is shown to hold global-in-time in the perturbative framework.The key point in our analysis is to deduce certain a priori estimates which are independent of the light speed and the main difficulty is due to the degeneracy of the dissipative effect of the electromagnetic field for large light speed.
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 decay with specular-reflection boundary condition when an initial datum is near Maxwellian equilibrium. We provide the compatible specular boundary condition for high-order derivatives and a velocity weighted energy estimate.
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 global in time classical solutions to the Cauchy problem near Maxwellians.
The spectrum structures and behaviors of the Vlasov-Maxwell-Boltzmann (VMB) systems for both two species and one species are studied in this paper. The analysis shows the effect of the Lorentz force induced by the electro-magnetic field leads to some different structure of spectrum from the classical Boltzmann equation and the closely related Vlasov-Poisson-Boltzmann system. And the significant difference between the two-species VMB model and one-species VMB model are given. The structure in high frequency illustrates the hyperbolic structure of the Maxwell equation. Furthermore, the long time…
A moderately thick spray can be described by a coupled system of equations consisting of the incompressible Navier-Stokes equations and the Vlasov-Boltzmann equation. We investigate this kind of mathematical model in this paper. In particular, we study the initial value problem for the Navier-Stokes-Vlasov-Boltzmann equations. The existence of global weak solutions is established by a weak convergence method. The interesting point of our main result is to handle the model with some breakup effects while the velocity of particles is in the whole space.
We establish the existence of renormalized solutions of the Vlasov-Maxwell-Boltzmann system with a defect measure in the presence of long-range interactions. We also present a control of the defect measure by the entropy dissipation only, which turns out to be crucial in the study of hydrodynamic limits.
We consider the homogeneous and inhomogeneous Landau equation for very soft and Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not exist under mild decay assumptions on the profile. We extend our analysis to the Vlasov-Poisson-Landau system and to the Boltzmann equation without angular cut-off.
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 the global strong solution to the unipolar VPB system towards the solution to an incompressible Navier-Stokes-Poisson-Fourier system based on the spectral analysis with precise estimation on the initial layer.
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 the Vlasov-Maxwell-Blotzmann equations over any periodic spatial domain in $\R^3$ is studied. It is shown that any properly scaled sequence of renormalized solutions of the Vlasov-Maxwell-Boltzmann equations has fluctuations that (in the weak $L^1$ topology) converge to an infinitesimal Maxwellian with fluid variables that satisfy the incompressibility and B…
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 field governed by the self-consistent Poisson equation plays a key role in the analysis so that the spectrum structure is genuinely different from the well-known one of the Boltzmann equation. Based on this, we give the optimal time decay rates of solutions to the equilibrium.
Global compressible Euler-Poisson limit of the ionic Vlasov-Poisson-Boltzmann system for all cutoff potentials
本文研究了离子Vlasov-Poisson-Boltzmann系统在全截断势范围下的可压缩Euler-Poisson极限，通过截断Hilbert展开和加权框架证明了解的全局收敛性。
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 is known for soft potential from [15]. However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0$. This gives the regularity to…
The Cauchy problem for the Vlasov-Maxwell-Boltzmann equations (VMB) is considered. First the renormalized solution to the Vlasov equation with the Lorentz force is discussed and the difficulty on the partial differentiability of the coefficients is overcome. Then the weak stability of the renormalized solutions to the Cauchy problem of VMB is established using the compactness of velocity averages and a renormalized formulation. Furthermore, the large time behavior of the renormalized solutions to VMB is studied and it is proved that the density of particles tends to a local Maxwellian as the t…
In the present paper, we consider the initial value problem for the bipolar Vlasov-Poisson-Boltzmann (bVPB) system and its corresponding modified Vlasov-Poisson-Boltzmann (mVPB). We give the spectrum analysis on the linearized bVPB and mVPB systems around their equilibrium state and show the optimal convergence rate of global solutions. It was showed that the electric field decays exponentially and the distribution function tends to the absolute Maxwellian at the optimal convergence rate $(1+t)^{-3/4}$ for the bVPB system, yet both the electric field and the distribution function converge to e…
The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian
本文研究无角截断的Vlasov-Poisson-Boltzmann系统与库仑势的Vlasov-Poisson-Landau系统，在多项式加权Sobolev空间中建立解的整体存在性、唯一性及大时间行为，证明依赖半群方法的额外耗散与静电场能量估计。
The Vlasov-Maxwell-Boltzmann/Landau system with polynomial perturbation near Maxwellian
本文研究麦克斯韦分布附近多项式扰动下的Vlasov-Maxwell-Boltzmann/Landau系统，通过Duhamel原理和时间衰减分析，证明了多项式加权空间中解的整体存在性、唯一性及大时间行为。
Green's Function and Pointwise Space-time Behaviors of the three-Dimensional modified Vlasov-Poisson-Boltzmann System
研究了三维修正Vlasov-Poisson-Boltzmann系统的格林函数的点wise时空行为，证明了低频下格林函数分解为宏观扩散波和Huygens波，速度为√(8/3)，并建立了非线性修正Vlasov-Poisson-Boltzmann系统的全局解的点wise时空估计。
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. This paper is concerned with the electron dynamics of kinetic plasmas in the whole space when the positive charged ion flow provides a spatially uniform background. We establish the global existence and optimal convergence rates of solutions near a global Maxwellian to the Cauchy problem on the Vlasov-Poisson-Boltzmann system for angular cutoff soft potenti…
Diffusive Limit of the One-species Vlasov-Maxwell-Boltzmann System for Cutoff Hard Potentials
本文通过引入新权函数的加权能量方法，解决了截断硬势全范围下单物种 Vlasov-Maxwell-Boltzmann 系统在扰动框架下的扩散极限问题，并建立了关于 Knudsen 数的全局时间一致性估计，首次实现了解的全局存在性与流体力学极限。
Global classical solutions to the ionic Vlasov-Poisson-Boltzmann system in a 3D periodic box
本文研究了三维周期箱中离子Vlasov-泊松-玻尔兹曼系统的全局经典解问题，通过非线性能量方法和新coercivity不等式，证明了在小初始扰动下存在唯一具有指数衰减的全局解。
The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov- Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the diffusion wave, the Huygens's type sound wave, the singular kinetic wave and the remainder term decaying exponentially in space-time. These behaviors are similar to the Boltzmann equation (Liu and Yu in Comm. Pure Appl. Math. 57: 1543-1608, 2004). Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the …
In this paper, we justify the convergence from the two-species Vlasov-Poisson-Boltzmann (in briefly,VPB) system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson (in briefly, NSFP) system with Ohm's law in the context of classical solutions. We prove the uniform estimates with respect to the Knudsen number $\varepsilon$ for the solutions to the two-species VPB system near equilibrium by treating the strong interspecies interactions. Consequently, we prove the convergence to the two-fluid incompressible NSFP as $\varepsilon$ go to 0.
This paper is devoted to the approximation of the linear Boltzmann equation by fractional diffusion equations. Most existing results address this question when there is no external acceleration field. The goal of this paper is to investigate the case where a given acceleration field is present. The main result of this paper shows that for an appropriate scaling of the acceleration field, the usual fractional diffusion equation is supplemented by an advection term. Both the critical and supercritical case are considered.
We prove a global-in-time limit from the two-species Vlasov-Maxwell-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. Besides the techniques developed for the classical solutions to the Vlasov-Maxwell-Boltzmann equations in the past years, such as the nonlinear energy method and micro-macro decomposition are employed, key roles are played by the decay properties of both the electric field and the wave equation with linear damping of the divergence free magnetic field. This is a companion paper of [N. Jiang and Y.-L. Luo, \emph{Ann. PDE} 8 (20…
This paper is concerned with the Vlasov-Poisson-Boltzmann system for plasma particles of two species in three space dimensions. The Boltzmann collision kernel is assumed to be angular non-cutoff with $-3<γ<-2s$ and $1/2\leq s<1$, where $γ$, $s$ are two parameters describing the kinetic and angular singularities, respectively. We establish the global existence and convergence rates of classical solutions to the Cauchy problem when initial data is near Maxwellians. This extends the results in \cite{DYZ-h, DYZ-s} for the cutoff kernel with $-2\leq γ\leq 1$ to the case $-3<γ<-2$ as long as the ang…
Diffusion Limit with Optimal Convergence Rate of Classical Solutions to the Vlasov-Maxwell-Boltzmann System
本文研究近 Maxwell 初值下 VMB 系统强解的扩散极限，通过新的解分解刻画初始层并结合谱分析，证明其收敛至 Navier-Stokes-Maxwell 系统且达到最优速率。
For the one-species Vlasov-Poisson-Boltzmann (VPB) system in the scaling under which the moments of the fluctuations formally converge to the incompressible Navier-Stokes-Fourier-Poisson (NSFP) system, we prove the uniform estimates with respect to the Knudsen number $ε$ for the fluctuations. As a consequence, the existence of the global-in-time classical solutions of VPB with all $ε\in (0,1]$ is established in whole space under small size of initial data, and the convergence to incompressible NSFP as $ε$ go to 0 is rigorously justified.
Diffusion Limit with Optimal Convergence Rate of Classical Solutions to the modified Vlasov-Poisson-Boltzmann System
研究修正Vlasov-泊松-玻尔兹曼系统经典解的扩散极限，通过谱分析证明了强解向不可压缩纳维-斯托克斯-泊松-傅里叶系统解的收敛性及收敛速率，对初始层进行了精确估计。
Diffusion Limit and the optimal convergence rate of the classical solution to the one-species Vlasov-Maxwell-Boltzmann system
本文基于谱分析技术研究单物种 Vlasov-Maxwell-Boltzmann 系统强解的扩散极限，证明了其经典解向不可压 Navier-Stokes-Maxwell 系统解的收敛性及收敛速率，并给出了初始层的精确估计。
For the Vlasov-Poisson-Boltzmann equations with random uncertainties from the initial data or collision kernels, we proved the sensitivity analysis and energy estimates uniformly with respect to the Knudsen number in the diffusive scaling using hypocoercivity method. As a consequence, we also justified the incompressible Navier-Stokes-Poisson limit with random inputs. In particular, for the first time, we obtain the precise convergence rate {\em without} employing any results based on Hilbert expansion. We not only generalized the previous deterministic Navier-Stokes-Poisson limits to random i…
Diffusive limit of the Vlasov-Poisson-Boltzmann system with cutoff soft potentials $-3<γ<0$ in the perturbative framework around global Maxwellian still remains open. By introducing a new weighted $H_{x,v}^2$-$W_{x,v}^{2, \infty}$ approach with time decay, we solve this problem for the full range of cutoff potentials $-3<γ\leq 1$. The core of this approach lies in the interplay between the velocity weighted $H_{x,v}^2$ energy estimate with time decay and the time-velocity weighted $W_{x,v}^{2,\infty}$ estimate with time decay for the Vlasov-Poisson-Boltzmann system, which leads to the uniform …
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 potentials has been an open problem. This is mainly due to the complex structure of the system, in particular, the degenerate dissipation at large velocity, the velocity-growth of the nonlinear term induced by the Lorentz force, and the regularity-loss of the electromagnetic fields. This paper aims to resolve this problem in the whole space provided that in…
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 boundary condition. The construction is based on an $L^{2}$-$L^{\infty}$ framework with a novel \textit{nonlinear-normed energy estimate} of a distribution function in weighted $W^{1,p}$-spaces and a $C^{2,δ}$-estimate of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellia…
The non-cutoff Vlasov-Poisson-Boltzmann system with weak collisions
本文研究弱碰撞非截断 Vlasov-Poisson-Boltzmann 系统，提出速度加权能量与向量场方法，证明 Maxwell 分布附近光滑解全局存在，并获得增强耗散及密度和电场的 Landau 阻尼。
The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^\infty$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^\infty$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate.
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 macroscopic quantities given by rarefaction wave solution of one-dimensional compressible Euler equations, we establish the time-asymptotic stability of planar rarefaction wave solutions for the Cauchy problem to VPB system with periodic or specular-reflection boundary condition. In particular, we successfully introduce physical boundaries, namely, specular-reflec…
Green's function and Pointwise Behavior of the One-Dimensional Vlasov-Maxwell-Boltzmann System
本文研究一维非线性 VMB 系统 Green 函数的逐点时空结构，识别出特有的高频双曲波与奇异短波，并据此建立全局解的逐点估计。
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 \cite{Deng-Ionescu-Pausader-ARMA-2017}, we establish the global-in-time validity of its Hilbert expansion and derive the limiting relativistic Euler-Maxwell system as the mean free path goes to zero. Our method is based on the $L^2-L^{\infty}$ framework and the Glassey-Strauss Representation of the electromagnetic field, with auxiliary $H^1$ estimate and $W^{1,…
Global stability of vacuum for the relativistic Vlasov-Maxwell-Boltzmann system
本文研究了相对论性Vlasov-Maxwell-Boltzmann系统中真空的全局稳定性，通过向量场方法和Glassey-Strauss分解，证明了小初始数据下的非线性稳定性。
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff intermolecular interactions, although there are some progress on the construction of global smooth solutions to its Cauchy problem near Maxwellians recently, the problem for the case of very soft potentials remains unsolved. By introducing a new time-velocity weighted energy method and based on some new optimal temporal decay estimates on the solution itself a…
Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System
本文研究环面或有限通道中Vlasov-Poisson-Landau/Boltzmann系统在低正则性初值下小振幅解的全局存在性与长时间行为，将Duan-Liu-Sakamoto-Strain的结果从纯Landau/Boltzmann方程推广至VPL和VPB系统。
Stationary Vlasov-Poisson-Boltzmann system in a convex domain
研究有界凸区域中受约束外势场影响的稳态和动态Vlasov-Poisson-Boltzmann系统，通过构建$W^{1,p}_{x,v}$-$\alpha C^1_{x,v}$自举框架和利用外势场结构推导无权重$C^1_v$估计，证明了稳态解的唯一性，并建立了小扰动下动态解的全局存在唯一性和指数收敛性。
Diffusive Limit of the Vlasov-Poisson-Boltzmann System without Angular Cutoff
该研究通过带新权函数的加权能量方法，解决了全范围非截断势下无角截断Vlasov-Poisson-Boltzmann系统的扩散极限问题，得到全局解存在性及流体动力学极限，拓展了已有结果的适用范围。
This work concerns the global existence of the weak solutions to a system of partial differential equations modeling the evolution of particles in the fluid. That system is given by a coupling between the standard isentropic compressible Navier-Stokes equations for the macroscopic description of a gas fluid flow, and a Vlasov-Boltzmann type equation governing the evolution of spray droplets modeled as particles with varying radius. We establish the existence of global weak solutions with finite energy, whose density of gas satisfies the renormalized mass equation. The proof, is partially motiv…
Global Hilbert expansion for the ionic Vlasov-Poisson-Boltzmann system
该研究通过严格推导证明了离子维拉索-泊松-波尔兹曼系统在克努尔森数趋近于零时的全局有效性，并揭示了截断希尔伯特展开的多层数学结构。
Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded convex domain with in-flow boundary condition. We establish the existence of strong solutions in the time interval $[0,T]$ for an arbitrary given $T>0$ when the initial distribution function is near an absolute Maxwellian. Our contribution is based on a new weighted energy estimate in some $W^{1,p}$ space and $L_x^3 L_v^{1+}$ space for soft potential. By using…
A Rigorous Derivation of the Vlasov-Navier-Stokes Model from Multicomponent Boltzmann Equations
该研究从双组分玻尔兹曼系统出发，在特定标度假设下严格推导不可压缩弗拉索夫-纳维-斯托克斯系统，为该模型的论证提供了关键理论支撑。
Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential
针对软势无角截断VPB系统，证明近Maxwellian初值下全空间Cauchy问题的全局正则性，覆盖$0<s<1$全范围，完善平滑效应，采用时间加权能量法与伪微分演算。
Diffusive Limit of the Vlasov-Maxwell-Boltzmann System without Angular Cutoff
该研究通过新权函数与无截断线性化Boltzmann算子各向异性耗散性的利用，解决了摄动框架下无截断Vlasov-Maxwell-Boltzmann系统的扩散极限问题，得到全局解存在性与流体动力学极限，覆盖此前所有可行参数范围。
We treat hydrodynamic limits of the Vlasov-Maxwell-Boltzmann system for one and two species of particles in a viscous incompressible regime.
Global Stability and Energy Growth in the Sheared Vlasov--Poisson--Boltzmann System
本文研究三维环面均匀剪切流下的Vlasov-Poisson-Boltzmann系统，结合多种分析方法证明自相似分布的全局稳定性，并推导零频系统得到剪切诱导能量增长的精确长时间描述。
We consider various sets of Vlasov-Fokker-Planck equations modeling the dynamics of charged particles in a plasma under the effect of a strong magnetic field. For each of them in a regime where the strength of the magnetic field is effectively stronger than that of collisions we first formally derive asymptotically reduced models. In this regime, strong anisotropic phenomena occur; while equilibrium along magnetic field lines is asymptotically reached our asymptotic models capture a non trivial dynamics in the perpendicular directions. We do check that in any case the obtained asymptotic model…
The incompressible Navier-Stokes-Fourier-Maxwell system limits of the Vlasov-Maxwell-Boltzmann system for soft potentials: the noncutoff cases and cutoff cases
该研究针对软势下的Vlasov-Maxwell-Boltzmann系统，分别在非截断（依赖强角度奇异性带来的速度耗散）和截断（采用新权函数与能量函数构造）情形下得到一致能量估计，证明了其向带欧姆定律的不可压缩Navier-Stokes-Fourier-Maxwell系统的极限。
In this work, the magnetohydrodynamics system is formally derived from two species Vlasov-Maxwell-Boltzmann system. By employing the hypocoercivity of the linear Boltzmann operator and overcoming the difficulties resulting from the singular Lorentz term, we first obtain the uniform estimates of solutions with respect to the Knudsen number and then derive the magnetohydrodynamics system from the dimensionless Valsov-Maxwell-Boltzmann system.
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 concerned with the rate of convergence of solutions to equilibrium for this system over ${\mathbb{R}}^3$. It is shown that the electric field which is indeed responsible for the lowest-order part in the energy space reduces the speed of convergence and hence the dispersion of this system over the full space is slower than that of the Boltzmann equation withou…
In this work, we mainly concern the limiting behavior of the electromagnetic field of two species Vlasov-Maxwell-Botlzmann system in diffusive limits. As knudsen numbers goes to zero, the electric magnetic and magnetic field may perserve or vanish. We verify rigorously Navier-Stokes, Navier-Stokes-Poisson and Navier-Stokes Maxwell limit of the two species Vlasov-Maxwell-Boltzmann system on the torus in three dimension. The justification is based on the unified and uniform estimates of solutions to the dimensionless Vlasov-Maxwell-Boltzmann. The uniform estimates of solutions are obtained by em…
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 with Ohm's law, we prove the uniform estimates with respect to Knudsen number $\eps$ for the fluctuations. As consequences, the existence of the global in time classical solutions of VMB with all $\eps \in (0,1]$ is established. Furthermore, the convergence of the fluctuations of the solutions of VMB to the classical solutions of NSFM with Ohm's law is rigoro…
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 its asymptotic behavior when the particle distribution function is a small perturbation around an arbitrarily large homogenous solution of the Boltzmann equation.
We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounded and integrable, and a point charge. Under some decay assumptions for the diffuse density close to the point charge, under bounds on the total energy, and assuming that the initial total diffuse charge is strictly less than one, we prove existence of global Lagrangian solutions. Our result extends the Eulerian theory of [16], proving that solutions are transported by the flow trajectories. The proof is based on the …
Hydrodynamic limit and Newtonian limit from the relativistic Vlasov-Maxwell-Boltzmann system to the classical Euler-Poisson system
本文在经典等熵可压缩Euler-Poisson系统全局光滑无旋解附近，构造了单物种相对论性Vlasov-Maxwell-Boltzmann系统的经典解，并严格证明了流体极限和牛顿极限到Euler-Poisson系统的结合。
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