Diogo Arsénio, Laure Saint-Raymond
We treat hydrodynamic limits of the Vlasov-Maxwell-Boltzmann system for one and two species of particles in a viscous incompressible regime.
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We study the asymptotic regime of strong electric fields that leads from the Vlasov-Poisson system to the Incompressible Euler equations. We also deal with the Vlasov-Poisson-Fokker-Planck system which induces dissipative effects. The originality consists in considering a situation with a finite total charge confined by a strong external field. In turn, the limiting equation is set in a bounded domain, the shape of which is determined by the external confining potential. The analysis extends to the situation where the limiting density is non-homogeneous and where the Euler equation is replaced…
Derivation of Yudovich solutions of Incompressible Euler from the Vlasov-Poisson system
本文通过调制能量方法，从Vlasov-Poisson方程推导出二维不可压缩欧拉方程，并提出一种能处理速度梯度仅为BMO的解的策略，与Yudovich定理相符。
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…
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.
The local existence and uniqueness of strong solutions for Cauchy problem of three-dimensional inhomogeneous incompressible Navier-Stokes-Vlasov equations
本文研究了三维不均匀不可压缩纳维-斯托克斯-维拉索方程柯西问题的强解的局部存在性和唯一性，通过线性化和近似解构造方法，丰富了强解的存在性结果。
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.
From Vlasov-Maxwell-Landau system with Coulomb potential to two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law
该研究在扩散区域中证明了带库仑势的Vlasov-Maxwell-Landau系统向带欧姆定律的双流体不可压缩NSFM系统的极限，并首次给出了全局时间一致Knudsen数估计。
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…
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…
We study the diffusive expansion for solutions around Maxwellian equilibrium and in a periodic box to the Vlasov-Maxwell-Boltzmann system, the most fundamental model for an ensemble of charged particles. Such an expansion yields a set of dissipative new macroscopic PDE's, the incompressible Vlasov-Navier-Stokes-Fourier system and its higher order corrections for describing a charged fluid, where the self-consistent electromagnetic field is present. The uniform estimate on the remainders is established via a unified nonlinear energy method and it guarantees the global in time validity of such a…
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。
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…
The incompressible inhomogeneous Navier-Stokes-Vlasov-Fokker-Planck equations: global well-posedness and inviscid limit
研究非均匀不可压缩流体-粒子相互作用系统，证明其全局适定性及无粘极限的强收敛性，并建立最优收敛速率。
The global well-posedness for the incompressible Navier-Stokes-Vlasov equations in two spatial dimensions is established by a priori estimates, the characteristic method and the semigroup analysis.
We are concerned with large-time behaviors of solutions for Vlasov--Navier--Stokes equations in two dimensions and Vlasov-Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the large-time behavior estimate for our main system and refine assumptions on the dimensions and a communication weight function. In particular, this allows us to take into account the effect of the misalignment interactions between particles. We then use a sharp heat kernel estimate to obtain the exponential time decay of fluid velocity to its average in $L^\infty$-…
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.
Global well-posedness and decay rates of strong solutions to the incompressible Vlasov-MHD system
本文研究了不可压缩Vlasov-MHD模型中强解的全局存在性与多项式衰减率，通过改进的能量方法和傅里叶技术克服了模型中缺乏耗散结构和强三阶耦合项的困难。
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.
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 Navier-Stokes system through the drag force. For the proposed kinetic-fluid model, we study the asymptotic regime corresponding to strong local alignment and diffusion forces. Under suitable assumptions on the initial data, we rigorously derive a coupled isothermal/pressureless Euler-Poisson system and incompressible Navier-Stokes system(in short, EPNS syste…
Fujita-Kato Solutions and Optimal Time Decay for the Vlasov-Navier-Stokes System in the Whole Space
本文研究了Vlasov-Navier-Stokes系统在全空间中的全局解构造及能量衰减，通过引入更高阶能量泛函，证明了小初始数据下的最优时间衰减率。
In this paper, we study the quasineutral limit (in other words the limit when the Debye length tends to zero) of Vlasov-Poisson like equations describing the behaviour of ions in a plasma. We consider massless electrons, with a charge density following a Maxwell-Boltzmann law. For cold ions, using the relative entropy method, we derive the classical Isothermal Euler or the (inviscid) Shallow Water systems from fluid mechanics. In a second time, we study the combined quasineutral and strong magnetic field regime for such plasmas.
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 …
We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier--Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. It is also shown that the weak solution, whos…
A Quantitative Hydrodynamic Limit for the Vlasov-Fokker-Planck/Navier-Stokes System in the Fine Particle Regime
本研究证明细粒子区域中Vlasov-Fokker-Planck/Navier-Stokes耦合系统的定量流体动力学极限，采用宏-微分解等方法消除小背景限制，获任意时间区间的显式逐点收敛率。
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。
The uniform-in-time electrostatic limit of the linearised Vlasov-Maxwell system: the Poisson equilibrium
本文证明线性化Vlasov-Maxwell系统在光速趋于无穷时，其解一致收敛于线性化Vlasov-Poisson解，误差为c^{-1}阶，并给出纵向Landau阻尼与横向Klein-Gordon色散机制。
Existence and partial regularity of suitable weak solutions to the 3D Navier-Stokes-Vlasov-Fokker-Planck equations
本文研究了三维纳维-斯托克斯-维拉科夫-福克-普朗克方程合适弱解的存在性与部分正则性，通过能量估计和局部能量不等式分析奇异性测度集的结构。
Modified compensating functions for the incompressible Euler--Vlasov--Fokker--Planck system: Global classical solutions and pointwise-in-space decay
研究全空间\(\mathbb R^3\)中不可压缩Euler - VFP系统柯西问题，通过用有限秩斜伴随修正增强经典补偿器，结合相关抵消与约束得出全局经典解，还构造泛函建立正阶和零阶衰减估计。
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…
Asymptotic behavior of the two-dimensional Vlasov-Poisson-Fokker-Planck equation with a strong external magnetic field
本文研究磁约束下VPFP方程在强外磁场中的长时间行为，证明其极限由欧拉型方程描述，均匀磁场下化为二维不可压缩欧拉方程的涡量形式，采用调制能量方法。
Derivation of the Vlasov-Maxwell system from the Maxwell-Schrödinger equations with extended charges
该研究针对库仑规范下带扩展电荷的Maxwell-Schrödinger方程，在半经典区域证明其收敛于非相对论Vlasov-Maxwell动力学并给出近似精度估计，同时建立了两类方程的适定性与正则性理论。
Backward problem for the 1D ionic Vlasov-Poisson equation
本文研究一维离子 Vlasov-Poisson 系统的反向问题，通过固定解的渐近行为证明了 Landau 阻尼。
The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101-113] and Dobrushin [Func. Anal. Appl. 13 (1979), 115-123] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy - i.e. the kinetic energy of the …
Vlasov equations can be formally derived from N-body dynamics in the mean-field limit. In some suitable singular limits, they may themselves converge to fluid dynamics equations. Motivated by this heuristic, we introduce natural scalings under which the incompressible Euler equations can be rigorously derived from N-body dynamics with repulsive Coulomb interaction. Our analysis is based on the modulated energy methods of Brenier and Serfaty.
A Probabilistic Mean-Field Limit for the Vlasov-Poisson System for Ions
本文基于概率方法，证明了离子维拉松-泊松系统可以从考虑热化电子的微观系统推导出来，解决了离子作为点电荷的均场极限问题。
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…
Modified scattering for small data solutions to the Vlasov-Maxwell system: a short proof
本文证明，在电磁场快速衰减条件下，Vlasov-Maxwell 系统紧支撑小数据全局解的分布函数具有修正散射行为，并覆盖 Glassey-Strauss 构造的所有小数据解。
The paper treats the validity problem of the nonrelativistic Vlasov-Poisson equation in $d\geq 2$ dimensions. It is shown that the Vlasov-Poisson dynamics can be derived as a combined mean field and point-particle limit of an N-particle Coulomb system of extended charges. This requires a sufficiently fast convergence of the initial empirical distributions. If the electron radius decreases slower than $N^{-\frac{1}{d(d+2)}}$, the corresponding initial configurations are typical. This result entails propagation of molecular chaos for the respective dynamics
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。
We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for one-dimensional bipolar Vlasov-Poisson-Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under the additional electrostatic potential force. Based on a new micro-macro type decomposition around the local Maxwellian related to the bipolar VPB system in our previous work [26], we prove that the superposition of a viscous contact wave and two rarefaction waves is time-asymptotically stable to 1D bipolar VPB system under some smallness cond…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of the third space dimension. We consider the case that the plasma is located in an infinitely long cylinder and is influenced by an external magnetic field. We prove existence of stationary solutions and give conditions on the external magnetic field under wh…
Large-time asymptotics of periodic two-dimensional Vlasov-Navier-Stokes flows
本文研究了二维Vlasov-Navier-Stokes流体在大时间下的渐进行为，证明了有限能量解向单速状态收敛，并探讨了初始粒子分布对收敛速度的影响。
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。
Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions
本文研究电子与离子两物种Vlasov-Poisson系统在Penrose稳定平衡态附近的线性Landau阻尼，推广了单物种结果，证明电场能量指数衰减。
The Semi-Classical Limit from the Dirac Equation with Time-Dependent External Electromagnetic Field to Relativistic Vlasov Equations
本文研究了狄拉克方程在$\hbar \to 0$极限下的半经典近似，通过非投影的威金斯方程推导出相对论维拉索方程，揭示了反物质和自旋的相对论效应。
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。
Due to ion-electron collisions, it is impossible to derive any two-fluid model for plasma as a direct hydrodynamic limit of the Vlasov-Poisson-Landau system for ions and electrons. At the same time, electrons are much lighter than their ion counterparts. In this work, we derive the massless electron limit of the Vlasov-Poisson-Landau system. This is done via a re-scaling of the electron velocity, leading to multiple velocity scales. Importantly, we demonstrate that ion-electron collisions vanish in this limit, due to special structure of the Landau collisions. We also show that this is invalid…
Motivated by recent models of current driven magnetization dynamics, we examine the coupling of the Landau-Lifshitz-Gilbert equation and classical electron transport governed by the Vlasov-Maxwell system. The interaction is based on space-time gyro-coupling in the form of emergent electromagnetic fields of quantized helicity that add up to the conventional Maxwell fields. We construct global weak solutions of the coupled system in the framework of frustrated magnets with competing first and second order gradient interactions known to host topological solitons such as magnetic skyrmions and hop…
A scaling limit for Vlasov equations with electrostatic fluctuations
本文研究了具有恒定磁场的等离子体Vlasov方程，通过在静电近似下引入电场白噪声扰动，证明了在适当的标度极限下会产生速度扩散，并探讨了其物理相关性。
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 reformulate a general class of classical bead-spring-chain models for dilute polymeric fluids, with Hookean spring potentials, as McKean-Vlasov diffusion. This results in a coupled system of partial differential equations involving the unsteady incompressible linearized Navier-Stokes equations, referred to as the Oseen system, for the velocity and the pressure of the fluid, with a source term which is a nonlinear function of the probability density function, and a second-order degenerate parabolic Fokker-Planck equation, whose transport terms depend on the velocity field, for the probabilit…
From relativistic Vlasov-Maxwell to electron-MHD in the quasineutral regime
该研究在解析正则性框架下推导相对论Vlasov-Maxwell系统的准中性极限，通过电磁场精细分解与色散校正子处理振荡效应，证明解强收敛至e-MHD系统，为等离子体建模常用的e-MHD约化提供首个严格强收敛的理论依据。
Scattering map for the Vlasov-Maxwell system around source-free electromagnetic fields
本研究针对无源电磁场周围的Vlasov-Maxwell系统，构造修正波算子与等距修正散射算子，得到小数据散射映射，并给出一类初值分散、$L^p_{x,v}\ imes L^2_x$范数较大的全局解。
Low Mach number limit of the compressible Euler--Vlasov--Fokker--Planck system in the whole space
本文通过精细能量方法和修正声学变量，证明了全空间可压缩Euler--Vlasov--Fokker--Planck系统在低马赫数极限下以$\mathcal O(\varepsilon)$速率收敛到不可压缩系统，解决了流体-粒子模型间的连接问题。
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.
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.
Twisting in One Dimensional Periodic Vlasov-Poisson System
本文研究一维周期 Vlasov-Poisson 系统在稳定稳态附近的扭转与丝化现象，证明了电子分布函数及流图梯度的 L1 范数随时间增长，并确立了环面上一类离子密度下稳定稳态的存在性。
We study in this paper the non-relativistic limit from Vlasov-Maxwell to Vlasov-Poisson, which corresponds to the regime where the speed of light is large compared to the typical velocities of particles. In contrast with \cite{Asano-Ukai-86-SMA}, \cite{Degond-86-MMAS}, \cite{Schaeffer-86-CMP} which handle the case of classical solutions, we consider measure-valued solutions, whose moments and electromagnetic fields are assumed to satisfy some uniform bounds. To this end, we use a functional inspired by the one introduced by Loeper in his proof of uniqueness for the Vlasov-Poisson system \cite{…
Stability of Big Bang singularity for the Einstein-Maxwell-scalar field-Vlasov system in the full strong sub-critical regime
针对3+1维爱因斯坦-麦克斯韦-标量场-弗拉索夫系统，通过分析数学结构与设计精细论证，确定新强亚临界区域并证明该区域内卡斯纳解的非线性稳定性，扩展了相关系统的研究结果。
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