Young-Pil Choi, In-Jee Jeong
We consider the Vlasov-Manev-Fokker-Planck (VMFP) system in three dimensions, which differs from the Vlasov-Poisson-Fokker-Planck in that it has the gravitational potential of the form $-1/r - 1/r^2$ instead of the Newtonian one. For the VMFP system, we establish the global-in-time existence of weak solutions. The proof extends to several related kinetic systems.
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Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system
本文研究了Vlasov-Manev（VM）系统定态的轨道稳定性和爆破自相似解的存在性。该系统是一个动力学模型，它具有与经典Vlasov-Poisson系统相似的Vlasov结构，但与$-1/r- 1/r^2$（Manev势）中的势场耦合，而不是通常的$-1/r$中的引力势场，特别是势场不满足泊松方程，而是满足分数拉普拉斯方程.我们首先证明的轨道稳定性的基态类型的解决方案，这些解决方案被构造为最小的哈密顿量，以下的经典策略：紧凑的最小化序列和刚性的流。然而，在驱动这种分析，有两个数学障碍：第一个是有关的VM系统的解决方案，我们克服了施加一个亚临界条件的约束条件的变分问题可能爆破。第二个困难（也是最重要的）与欧拉-拉格朗日方程（分数-拉普拉斯方程）的性质有关，泊松方程的经典结果不适用于此。我们克服了这一困难，证明了唯一性的最小化equiometricability约束下，只使用的潜力，而不是分数拉普拉斯欧拉-拉格朗日方程本身的规律性。在本文的第二部分中，我们证明了Vlasov-Manev方程的精确自相似爆破解的存在性，其中初始数据任意接近基态。这种构造是基于一个合适的变分问题与等测约束。
We investigate the Cauchy problem for the Vlasov--Riesz system, which is a Vlasov equation featuring an interaction potential generalizing previously studied cases, including the Coulomb $Φ= (-Δ)^{-1}ρ$, Manev $(-Δ)^{-1} + (-Δ)^{-\frac12}$, and pure Manev $(-Δ)^{-\frac12}$ potentials. For the first time, we extend the local theory of classical solutions to potentials more singular than that for the Manev. Then, we obtain finite-time singularity formation for solutions with various attractive interaction potentials, extending the well-known blow-up result of Horst for attractive Vlasov--Poisson…
On the Vlasov-Poisson-Fokker-Planck equation near Maxwellian
通过时间上一致的能量估计和宏观方程，我们建立了Vlasov-Poisson-Fokker-Planck方程小振幅光滑解在全空间和周期盒中的指数时间衰减率.
Nonlinear Fokker-Planck equations with singular integral drifts and McKean-Vlasov SDEs
本文证明了Sobolev空间H^{-1}中具有奇异漂移的非线性Fokker-Planck方程的适定性，并给出了其在McKean-Vlasov方程强解存在性中的应用。
Fractional diffusion limit for a fractional Vlasov-Fokker-Planck equation
本文用分数阶拉普拉斯算子代替拉普拉斯算子，严格推导了Vlasov-Fokker-Planck方程的宏观极限。密度的演化由分数阶热方程控制，该方程中加入了来自外力的对流项。分析是由一个修改后的检验函数的方法，并通过获得二次熵界的先验估计。另外，我们还证明了Vlasov分数阶Fokker-Planck方程解的存在唯一性。
We consider the compressible Vlasov-Poisson-Fokker-Planck-Navier-Stokes system in a three dimensional bounded domain with nonhomogeneous Dirichlet boundary conditions. The system describes the evolution of charged particles ensemble dispersed in an isentropic fluid. For the adiabatic coefficient $γ>3/2$, we establish the global existence of weak solutions to this system with arbitrary large initial and boundary data.
This paper is devoted to the linearized Vlasov-Poisson-Fokker-Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov-Poisson-Fokker-Planck system without any small mass assumption.
In the present paper, we study the diffusion limit of the classical solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system with initial data near a global Maxwellian. We prove the convergence and establish the optimal convergence rate of the global strong solution to the VPFP system towards the solution to the drift-diffusion-Poisson system based on the spectral analysis with precise estimation on the initial layer.
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 referred to as aggregation-diffusion equations. We show that a weak solution to the Vlasov--Poisson--Fokker--Planck system strongly converges to a strong solution to the diffusive model. Our proof relies on the modulated macroscopic kinetic energy estimate based on the weak-strong uniqueness principle together with a careful analysis of the Poisson equation.
We establish a quantitfied overdamped limit for kinetic Vlasov-Fokker-Planck equations with nonlocal interaction forces. We provide explicit bounds on the error between solutions of that kinetic equation and the limiting equation, which is known under the names of aggregation-diffusion equation or McKean-Vlasov equation. Introducing an intermediate system via a coarse-graining map, we quantitatively estimate the error between the spatial densities of the Vlasov-Fokker-Planck equation and the intermediate system in the Wasserstein distance of order 2. We then derive an evolution-variational-lik…
Global existence of weak solutions to the nonlinear Vlasov-Fokker-Planck equation
本文证明了固定碰撞频率的非线性Vlasov-Fokker-Planck方程在大初始数据下弱解的全局存在性，并验证了守恒律与H-定理。
Global Classical Solutions of the one and one-half dimensional Vlasov-Maxwell Fokker-Planck System
本文研究了“一又二分之一”维Vlasov-Maxwell-Fokker-Planck系统，得到了第一个关于解的适定性的结果。具体地说，我们证明了在大的经典解的柯西问题和增益的分布函数在其动量参数的正则性的整体时间的存在性和唯一性。
Instability in a Vlasov-Fokker-Planck binary mixture
本文针对描述两类粒子与势场、定温热库相互作用演化的Vlasov-Fokker-Planck动力学模型，证明了低温下均匀平衡态在特定扰动下的动态不稳定性，研究受相关文献问题启发。
On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential
我们证明了具有低正则性初值的Vlasov-Poisson-Fokker-Planck系统的整体解的存在性，并证明了具有小的非线性项但可能具有大的外约束势的Vlasov-Poisson-Fokker-Planck系统在$d=2$和$d=3$维上的平衡态的趋势.证明依赖于一个不动点参数使用尖锐的估计（在短期和长期时间尺度）的半群相关的福克-普朗克算子，这是由第一作者获得。
Global Existence for the "One and one-half" dimensional relativistic Vlasov-Maxwell-Fokker-Planck system
在最近的一篇论文中，Calogero和Alcantara导出了一个洛伦兹不变的Fokker-Planck方程，该方程对应于与相对论性布朗运动相关的粒子分布的演化。我们研究了这个问题的“一个半”维版本的非线性电磁相互作用-相对论性弗拉索夫-麦克斯韦-福克-普朗克系统-并获得了第一个结果有关的适定性的解决方案。具体地说，我们证明了柯西问题的经典解的全局时间存在性和唯一性，以及在其动量参数中分布函数的正则性。
We study a hydrodynamic limit of a system of coupled kinetic and fluid equations under a strong local alignment force and a strong Brownian motion. More precisely, we consider the Vlasov-Fokker-Planck type equation and compressible Navier-Stokes equations with a density-dependent viscosity. Based on a relative entropy argument, by assuming the existence of weak solutions to that kinetic-fluid system, we rigorously derive a two-phase fluid model consisting of isothermal Euler equations and compressible Navier-Stokes equations with a density-dependent viscosity.
The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three dimension are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.
In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\mathbb T^d \times \mathbb R^d$. Initial conditions are taken $H^σ$ with $σ> d/2 + 1$ (in addition to polynomial velocity weights). We additionally show that solutions to the VPFP are instantly $C^\infty_{x,v}$ due to hypoelliptic regularization if the external force fields are smooth. The external forcing arises in the kinetic equation as a stochastic transport in velocit…
Global existence and vanishing viscosity limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck system in critical spaces
本文在临界Besov空间中证明可压缩Navier-Stokes-Vlasov-Fokker-Planck系统强解的存在唯一性，建立一致正则性估计并验证以O(ε)速率收敛的消失粘性极限，同时获得最优时间衰减率。
Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
本文针对等离子体磁约束问题，研究强外磁场下Vlasov-Maxwell-Fokker-Planck系统的长时间行为，推导渐近简化模型并在二维空间三维速度维度下证明其适定性，为系统提供严格数学证明。
The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime
本文研究弱扩散与相对论速度奇异性下的空间非齐次 Vlasov-Nordström-Fokker-Planck 方程组，证明无摩擦 Cauchy 问题相对齐次系统动态稳定，并给出全局经典解、渐近行为及自相似框架下的稳定性。
Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces
本文研究了具有局部定向力的Vlasov-Fokker-Planck方程的整体适定性和时间渐近衰减。该方程可以从一个基于主体的自组织动力学模型（带噪声的Motsch-Tadmor模型）中形式化地推导出来。在整体Maxwell空间上证明了该方程的整体经典解的存在唯一性。对于大时间的行为，我们显示的代数衰减率的解决方案，在适当的假设下，对初始数据的平衡。我们还注意到，当空间域是周期性的时，收敛速率是指数的。本文使用的主要方法是经典能量估计与双曲-抛物耗散参数相结合。
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。
Global weak solutions for compressible Navier-Stokes-Vlasov-Fokker-Planck system
本文研究了一维可压缩Navier-Stokes-Vlasov-Fokker-Planck系统，在空间周期域中建立了全局弱解的存在性、唯一性与正则性，并证明了随时间演化粒子分布收敛于Maxwellian分布且流体与粒子宏观速度趋于一致。
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…
Well-posedness and trend to equilibrium for the Vlasov-Poisson-Fokker-Planck system with a confining potential
该研究针对带外部约束势的Vlasov-Poisson-Fokker-Planck系统，借助Lyapunov泛函、线性化系统新估计及不动点方法，证明了加权Sobolev空间中mild解的存在唯一性，以及解向全局平衡态的指数收敛性，且收敛速率估计显式可构造。
Propagation of moments and uniqueness of weak solutions to the Vlasov-Poisson-Fokker-Planck system
在本文中，我们证明了$C([0,T]; L^p)$中Vlasov-Poisson-Fokker-Planck方程组的弱解的唯一性，假设解有一个局部有界密度，该密度以一个“合理”的速率趋于无穷大，如$t\to 0$。作为推论，我们得到了初始数据$f_0$满足$f_0|v|^2\in L^1$时的弱解的唯一性，解决了有限能量下的弱解的唯一性问题.此外，我们还证明了相对于速度的力矩可以传播到高于2的任何阶次。
Diffusive limit of the Vlasov-Poisson-Fokker-Planck model: quantitative and strong convergence results
本研究针对Vlasov-Poisson-Fokker-Planck模型的扩散极限，推导了无维数限制的先验估计，得到L2空间强收敛及接近最优的显式收敛速率，结果在趋于无穷的有界时间区间上成立。
Weak collision effect on nonlinear Landau damping for the Vlasov-Poisson-Fokker-Planck system
本文研究环面上Vlasov-Poisson-Fokker-Planck系统中弱碰撞对非线性Landau阻尼的影响，针对不同Gevrey指标建立了小初值的全局稳定性与增强耗散，并揭示了相位混合、增强耗散和等离子体回声的作用。
This paper is concerned with a kineitc-fluid model with random initial inputs in the fine particle regime, which is a system coupling the incompressible Navier-Stokes equations and the Vlasov-Fokker-Planck equations that model dispersed particles of different sizes. A uniform regularity for random initial data near the global equilibrium is established in some suitable Sobolev spaces by using energy estimates, and we also prove the energy decays exponentially in time by hypocoercivity arguments, which means that the long time behavior of the solution is insensitive to the random perturbation i…
Hydrodynamic limit of the Vlasov-Poisson-Fokker-Planck system in low-field regime
本文研究低场极限下VPFP系统流体极限，通过矩方法推导DDP系统并严格证明其收敛性，利用高阶能量估计方法确保解的全局适定性。
Well-posedness and long-time behavior for self-consistent Vlasov-Fokker-Planck equations with general potentials
本文研究了具外部约束势和非线性自洽相互作用的 Vlasov-Fokker-Planck 方程的适定性及长时间行为，通过引入新相互作用核条件，结合 hypocoercivity 理论设计 Lyapunov 泛函，证明了在低正则性下解的指数衰减及稳态稳定性。
Modulated Gibbs Measure and Mean-Field Limit for 3D Vlasov--Poisson--Fokker--Planck Equations
本文通过引入调制Gibbs测度并结合加权BBGKY估计，首次在短时间区间上为三维VPFP方程建立了无截断的均值场极限与混沌传播。
We study an asymptotic analysis of a coupled system of kinetic and fluid equations. More precisely, we deal with the nonlinear Vlasov-Fokker-Planck equation coupled with the compressible isentropic Navier-Stokes system through a drag force in a bounded domain with the specular reflection boundary condition for the kinetic equation and homogeneous Dirichlet boundary condition for the fluid system. We establish a rigorous hydrodynamic limit corresponding to strong noise and local alignment force. The limiting system is a type of two-phase fluid model consisting of the isothermal Euler system and…
A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
本文提出了一种基于BBGKY层级新估计的方法，首次推导出2维等离子体Vlasov-Poisson-Fokker-Planck系统的平均场极限，并适用于奇异相互作用核。
On a Vlasov-Fokker-Planck equation for stored electron beams
本文研究了描述同步加速器储存环中电子束纵向动力学的自洽 Vlasov-Fokker-Planck 方程，证明了全局经典解的存在唯一性、稳态的存在性，并在小束流电流下证明了稳态的局部渐近非线性稳定性。
Convergence of a system of particles, interacting with a fluid, to Navier-Stokes-Vlasov-Fokker-Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov-Fokker-Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier-Stokes component. A new uniqueness result for the PDE system is added.
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。
Strong solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck equations: Global existence near the equilibrium and large time behavior
考虑了描述分散两相流演化的动力学流体模型。该模型由颗粒（分散相）的Vlasov-Fokker-Planck方程和流体（流体相）的可压缩Navier-斯托克斯方程通过摩擦力耦合而成。摩擦力取决于密度，这与许多以前对动力学流体模型的研究不同，在建模中更具物理性，但在分析中明显更困难。介绍了处理流体与颗粒间强耦合问题的新方法和新技术。当初值为某一给定平衡点的小扰动时，证明了三维全空间中强解的整体适定性。此外，还得到了解向平衡态收敛的代数收敛速率。对于周期域，当收敛速度为指数时，同样的全局适定性结果仍然成立。
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。
Quantitative light-particle limit for the Vlasov-Fokker-Planck-Navier-Stokes system
采用相对熵方法，针对轻粒子区域中粒子弛豫在奇异快时间尺度上的Vlasov-Fokker-Planck-Navier-Stokes系统，首次建立了轻粒子极限的定量收敛理论，给出了动力学分布和流体速度的显式收敛速率，并得到了负Sobolev空间中宏观密度和流体速度的精细估计。
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。
This work is concerned with the existence of mild solutions to non-linear Fokker-Planck equations with fractional Laplace operator $(-Δ)^s$ for $s\in\left(\frac12,1\right)$. The uniqueness of Schwartz distributional solutions is also proved under suitable assumptions on diffusion and drift terms. As applications, weak existence and uniqueness of solutions to McKean-Vlasov equations with Lévy-Noise, as well as the Markov property for their laws are proved.
This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov-Fokker-Planck equation towards the aggregation-diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation of the weak convergence of the corresponding stochastic differential equations (SDEs) of Mckean type in the continuous path space. We show that one can obtain the same convergence rate as in [10] under the same assumptions.
Trend to equilibrium for a delay Vlasov-Fokker-Planck equation and explicit decay estimates
本文研究了一类随机相互作用时滞粒子系统的时滞Vlasov-Fokker-Planck方程。在一定的参数限制条件下，证明了平均场方程的适定性和遍历性，并证明了只要时滞有限，该方程以指数收敛速率收敛到唯一的稳态解.对于无限延迟，即，当考虑所有解路径的历史时，示出了解的多项式衰减。
Landau damping, collisionless limit, and stability threshold for the Vlasov-Poisson equation with nonlinear Fokker-Planck collisions
本文研究小碰撞频率下 VPFP 方程，证明 Gevrey 类扰动可引发 Landau 阻尼与增强耗散，给出稳定性阈值上界，并证明短时间内解收敛到无碰撞 Vlasov-Poisson 方程的解。
Diffusion limit for Vlasov-Fokker-Planck Equation in bounded domains
本文在有界空间区域中导出了具有镜面反射型边界条件的动力学Vlasov-Fokker-Planck方程的扩散近似。证明的方法涉及到一个特定的一类检验函数的建设中选择的弱制定的动力学模型。这涉及到分析的基础动力学方程的哈密顿动力学耦合在边界处的反射定律。这种方法只要求解族在某个加权希尔伯特空间中是弱紧的，而不需要复杂的$\mathrm L^1$设置。
Weakly inhomogeneous solutions to a nonlinear Vlasov--Fokker--Planck equation in a domain
研究有界域内带镜面反射边界的非线性Vlasov-Fokker-Planck方程，证明初始数据接近径向空间齐次函数时存在全局弱解并以指数速率衰减至Maxwellian，通过正则化与线性系统逼近实现。
From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge
我们研究了从Vlasov-Poisson系统到不可压缩Euler方程的强电场的渐近状态。我们还讨论了引起耗散效应的Vlasov-Poisson-Fokker-Planck系统。独创性在于考虑一个有限的总电荷的情况下，由一个强大的外部领域。反过来，限制方程被设置在一个有界的区域，其形状是由外部限制电位。分析扩展到极限密度是非均匀的情况，其中欧拉方程被湖方程（也称为滞弹性方程）取代。
Propagation of chaos for the Vlasov-Poisson-Fokker-Planck system in 1D
我们考虑一个一维的粒子系统，通过排斥或吸引库仑力相互作用。我们证明了分子混沌向与Vlasov-Poisson-Fokker-Planck方程相关联的非线性混沌的标量传播。我们得到了期望收敛的一个定量估计，最佳收敛速度为$N^{-1/2}$阶。我们还证明了相关的经验测度的指数集中不等式。一个关键的论点是（非线性）VPFP方程的弱-强稳定性估计，我们能够适应粒子系统在某种意义上。
GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles
在本文中，我们讨论了伏拉索夫-福克-普朗克方程和底层微观粒子系统之间的联系，并在GENERIC框架下解释了这些联系（Öttinger 2005）。这种解释提供了（a）GENERIC系统的变分公式，（b）洞察这种变分公式的起源，以及（c）GENERIC放置在其构成元素上的条件的起源的解释，特别是所谓的简并性或非相互作用条件。这项工作表明，大偏差原则，一方面和梯度流结构，另一方面扩展到不可逆的粒子系统之间的一般连接。
Global well-posedness and inviscid limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent friction force
本文研究了压缩性纳维-斯托克斯-维拉科夫-福克-计划克系统中密度依赖摩擦力的全局well-posed性及无粘极限，首次证明了经典解的全局存在性，并揭示了流体-粒子相互作用诱导的新型松弛机制。
Quantitative approximation of the Vlasov(-Fokker-Planck)-Navier-Stokes system by stochastic particle systems
本文研究了通过拖曳力耦合的不可压缩纳维-斯托克斯方程与Vlasov(-Fokker-Planck)方程组成的流体-粒子系统，证明了粒子系统在N趋近于无穷大时向Vlasov(-Fokker-Planck)-Navier-Stokes系统收敛的速率。
The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium
本文研究了非凸约束势下Vlasov-Fokker-Planck方程解的长时间行为。这是一个非局部非线性偏微分方程，描述了在非凸势、相互作用势、摩擦力和随机力的影响下运动的粒子的概率分布随时间的演化。使用自由能的方法，我们表明，在适当的假设下，解决方案的弗拉索夫-福克-普朗克方程收敛到一个不变的概率。
On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field
爱因斯坦-弗拉索夫-福克-普朗克系统描述了爱因斯坦广义相对论中自引力粒子的动力学扩散动力学。我们研究了Cauchy问题的空间齐次和各向同性的解决方案，并证明了存在的整体解决方案和解决方案，爆破在有限的时间取决于某些功能的初始数据的大小。我们还获得了信息的大时间行为的整体解决方案和对奇异的解决方案，在罚款时间爆破。我们的研究结果需要存在一个阶段的减速膨胀，然后是一个阶段的加速膨胀，按照宇宙学的物理预期。
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
本文考虑了一个Vlasov-Fokker-Planck方程，它描述了相互作用和扩散物质在位置和速度空间中密度的演化。我们使用概率的解释，以获得收敛到均衡Wasserstein距离与显式指数率。我们还证明了伴随粒子系统的混沌传播性质，并给出了粒子系统对解的逼近速度。最后，一个运输不等式的粒子系统的分布导致定量偏差边界上的近似方程的平衡解的经验平均值的粒子在给定的时间。
In this paper we study second order stochastic differential equations with measurable and density-distribution dependent coefficients. Through establishing a maximum principle for kinetic Fokker-Planck-Kolmogorov equations with distribution-valued inhomogeneous term, we show the existence of weak solutions under mild assumptions. Moreover, by using the Hölder regularity estimate obtained recently in \cite{GIMV19}, we also show the well-posedness of generalized martingale problems when diffusion coefficients only depend on the position variable (not necessarily continuous). Even in the non dens…
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit
本文研究了Vlasov-Poisson-Fokker-Planck方程在不同碰撞和非线性 regime下的长时间行为，通过非线性椭圆方程和超协调估计分析解的收敛性和衰减特性。
Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition
本文研究Vlasov-Fokker-Planck（VFP）方程的定态解集.该方程描述了在双势阱、相互作用势、摩擦力和随机力的影响下运动的粒子的概率分布随时间的演化。我们证明，在适当的假设下，VFP方程没有一个唯一的固定的解决方案，并存在一个相变。我们的研究依赖于Tugaut和合著者关于McKean-Vlasov方程的最新结果。
Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs
本文利用低强制性分析，证明了随机初始输入下多相 Navier-Stokes–Vlasov–Fokker–Planck 耦合系统双精度方法在动理学与流体动力学区域中的一致误差估计。
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