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Journal articles on the topic 'Vlassov equation'

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Published: 31 May 2025

Last updated: 31 July 2025

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1

BARTHELMÉ, RÉGINE, PATRICK CIARLET, and ERIC SONNENDRÜCKER. "GENERALIZED FORMULATIONS OF MAXWELL'S EQUATIONS FOR NUMERICAL VLASOV–MAXWELL SIMULATIONS." Mathematical Models and Methods in Applied Sciences 17, no. 05 (2007): 657–80. http://dx.doi.org/10.1142/s0218202507002066.

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When solving numerically approximations of the Vlasov–Maxwell equations, the source terms in Maxwell's equations coming from the numerical solution of the Vlasov equation do not generally satisfy the continuity equation which is required for Maxwell's equations to be well-posed. Hence it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. Different such formulations have been introduced previously. The aim of this paper is to perform their mathematical analysis and verify the existence and uniqueness of the solution.

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2

Mezerdi, Mohamed Amine. "On the construction of the solution of mean field stochastic differential equations driven by G-Brownian motion via small delays." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e8388. http://dx.doi.org/10.54021/seesv5n2-266.

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This work explores the strong convergence of the Carathéodory approximation scheme, for nonlinear mean-field stochastic differential equations called also McKean-Vlasov stochastic differential equations (MVSDEs), under the framework of G-Brownian motion. Note that the coefficients dependent on the state variable and its marginal distribution . This numerical scheme is defined by a series of stochastic processes described through the sequence of delayed McKean-Vlasov stochastic differential equations driven by G-Brownian motion. The benefit of the Carathéodory iteration scheme is its capability

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3

Vedenyapin, Victor, Nikolay Fimin, and Valery Chechetkin. "The system of Vlasov–Maxwell–Einstein-type equations and its nonrelativistic and weak relativistic limits." International Journal of Modern Physics D 29, no. 01 (2020): 2050006. http://dx.doi.org/10.1142/s0218271820500066.

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We considered derivation of Vlasov–Einstein–Maxwell system of equations from the first principles, i.e. using classical Maxwell–Einstein–Hilbert action principle. We know many papers in which the theories indicated as Einstein–Vlasov, Vlasov–Maxwell–Einstein, Einstein–Maxwell–Boltzmann are discussed, and we discuss difficulties of usually used equations. We use another way of derivation and obtain an alternative version based on the generalized Fock–Weinberg form of equation of motion.

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4

Vedenyapin, Victor Valentinovich, and Dmitry Aleksandrovich Kogtenev. "On Derivation and Properties of Vlasov-type equations." Keldysh Institute Preprints, no. 20 (2023): 1–18. http://dx.doi.org/10.20948/prepr-2023-20.

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Derivation of the gravity and electrodynamics equations in the Vlasov-Maxwell-Einstein form is considered. Properties of Vlasov-Poisson equation and its application to construction of periodic solutions – Bernstein-Greene-Kruskal waves – are proposed.

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5

Wang, Weifeng, Lei Yan, Junhao Hu, and Zhongkai Guo. "An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations." Journal of Mathematics 2021 (July 16, 2021): 1–11. http://dx.doi.org/10.1155/2021/8742330.

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In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.

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6

JIN, SHI, XIAOMEI LIAO, and XU YANG. "THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY." Journal of Hyperbolic Differential Equations 05, no. 03 (2008): 569–87. http://dx.doi.org/10.1142/s021989160800160x.

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In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation. We also numerically justify the multivalued solution given by a moment system of the Vlasov–Poisson equations as the semiclassical limit of the Schrödinger–Poisson equations.

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7

SALORT, DELPHINE. "TRANSPORT EQUATIONS WITH UNBOUNDED FORCE FIELDS AND APPLICATION TO THE VLASOV–POISSON EQUATION." Mathematical Models and Methods in Applied Sciences 19, no. 02 (2009): 199–228. http://dx.doi.org/10.1142/s0218202509003401.

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The aim of this paper is to give new dispersive tools for certain kinetic equations. As an application, we study the three-dimensional Vlasov–Poisson equation for initial data having strictly less than six moments in [Formula: see text] where the nonlinear term E is a priori unbounded. We prove via new dispersive effects that in fact the force field E is smooth in space at the cost of a localization in a ball and an averaging in time. We deduce new conditions to bound the density ρ in L∞ and to have existence and uniqueness of global weak solutions of the Vlasov–Poisson equation with bounded d

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8

EL-HANBALY, A. M., and A. ELGARAYHI. "Exact solutions of the collisional Vlasov equation." Journal of Plasma Physics 59, no. 1 (1998): 169–77. http://dx.doi.org/10.1017/s0022377897006132.

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The symmetry group of the Vlasov–Fokker–Planck equation (VFPE) is constructed. The effects of the Poisson equation on this group is studied, and different types of similarity solutions of the whole system of equations (VFPE+Poisson equation) are obtained.

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9

Larsson, Jonas. "An action principle for the Vlasov equation and associated Lie perturbation equations. Part 1. The Vlasov—Poisson system." Journal of Plasma Physics 48, no. 1 (1992): 13–35. http://dx.doi.org/10.1017/s0022377800016342.

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A new action principle determining the dynamics of the Vlasov–Poisson system is presented (the Vlasov–Maxwell system will be considered in Part 2). The particle distribution function is explicitly a field to be varied in the action principle, in which only fundamentally Eulerian variables and fields appear. The Euler–Lagrange equations contain not only the Vlasov–Poisson system but also equations associated with a Lie perturbation calculation on the Vlasov equation. These equations greatly simplify the extensive algebra in the small-amplitude expansion. As an example, a general, manifestly Man

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10

TARASOV, VASILY E. "LIOUVILLE AND BOGOLIUBOV EQUATIONS WITH FRACTIONAL DERIVATIVES." Modern Physics Letters B 21, no. 05 (2007): 237–48. http://dx.doi.org/10.1142/s0217984907012700.

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The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fractional generalization of the Hamiltonian systems is discussed. Fractional kinetic equation for the system of charged particles are considered.

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11

CARRILLO, JOSÉ A., and SIMON LABRUNIE. "GLOBAL SOLUTIONS FOR THE ONE-DIMENSIONAL VLASOV–MAXWELL SYSTEM FOR LASER-PLASMA INTERACTION." Mathematical Models and Methods in Applied Sciences 16, no. 01 (2006): 19–57. http://dx.doi.org/10.1142/s0218202506001042.

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We analyze a reduced 1D Vlasov–Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split into two terms: an electrostatic field obtained from Poisson's equation and a vector potential term satisfying a nonlinear wave equation. Both nonlinearities in the Poisson and wave equations are due to the coupling with the Vlasov equation through the charge density. We show global existence of weak solutions in the nonrelativistic case, and global existence of characteristic soluti

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12

Echeverría-Veas, Sebastián, Pablo S. Moya, Marian Lazar, and Stefaan Poedts. "First Principles Description of Plasma Expansion Using the Expanding Box Model." Universe 9, no. 10 (2023): 448. http://dx.doi.org/10.3390/universe9100448.

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Multi-scale modeling of expanding plasmas is crucial for understanding the dynamics and evolution of various astrophysical plasma systems such as the solar and stellar winds. In this context, the Expanding Box Model (EBM) provides a valuable framework to mimic plasma expansion in a non-inertial reference frame, co-moving with the expansion but in a box with a fixed volume, which is especially useful for numerical simulations. Here, fundamentally based on the Vlasov equation for magnetized plasmas and the EBM formalism for coordinates transformations, for the first time, we develop a first prin

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13

Larsson, Jonas. "An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system." Journal of Plasma Physics 49, no. 2 (1993): 255–70. http://dx.doi.org/10.1017/s0022377800016974.

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An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturba

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14

Ekiel-Jeżewska, Maria L., Tor Flå, and Allan N. Kaufman. "Modulated electromagnetic waves in relativistic plasmas: field and kinetic equations." Journal of Plasma Physics 53, no. 2 (1995): 185–212. http://dx.doi.org/10.1017/s0022377800018110.

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Modulated electromagnetic plane waves in relativistic collisionless, unmagnetized plasmas are investigated through expansion in a small parameter, corresponding to weak dispersion and weak nonlinearity. The oscillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A description in terms of the relativistic Vlasov equation for oscillation-centre distribution functions is introduced. A system of coupled field and kinetic eequations is obtained order by order.The final result is a generalized vector nonlineat schrödinger eq

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15

SMEREKA, PETER. "A Vlasov equation for pressure wave propagation in bubbly fluids." Journal of Fluid Mechanics 454 (March 10, 2002): 287–325. http://dx.doi.org/10.1017/s002211200100708x.

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The derivation of effective equations for pressure wave propagation in a bubbly fluid at very low void fractions is examined. A Vlasov-type equation is derived for the probability distribution of the bubbles in phase space instead of computing effective equations in terms of averaged quantities. This provides a more general description of the bubble mixture and contains previously derived effective equations as a special case. This Vlasov equation allows for the possibility that locally bubbles may oscillate with different phases or amplitudes or may have different sizes. The linearization of

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16

Goudon, T. "Asymptotic problems for a kinetic model of two-phase flow." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 6 (2001): 1371–84. http://dx.doi.org/10.1017/s030821050000144x.

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We consider asymptotic problems for coupled equations modelling interactions between particles and a viscous fluid. The particles are driven by a Vlasov-like equation, involving the velocity of the fluid. We obtain, as certain parameters tend to 0, hydrodynamic equations for the macroscopic density and the velocity.

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17

Marcos, Aboubacar, and Ambroise Soglo. "Solutions of a Class of Degenerate Kinetic Equations Using Steepest Descent in Wasserstein Space." Journal of Mathematics 2020 (June 9, 2020): 1–30. http://dx.doi.org/10.1155/2020/7489532.

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We use the steepest descent method in an Orlicz–Wasserstein space to study the existence of solutions for a very broad class of kinetic equations, which include the Boltzmann equation, the Vlasov–Poisson equation, the porous medium equation, and the parabolic p-Laplacian equation, among others. We combine a splitting technique along with an iterative variational scheme to build a discrete solution which converges to a weak solution of our problem.

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18

Holm, D. D., V. Putkaradze, and C. Tronci. "Double-bracket dissipation in kinetic theory for particles with anisotropic interactions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2122 (2010): 2991–3012. http://dx.doi.org/10.1098/rspa.2010.0043.

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We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double-bracket approach (double-bracket Vlasov, or DBV). The moments of the DBV equation lead to a non-local form of Darcy’s law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double-bracket kinetic equations is expressed as Lie–Darcy continuum equations for densities of mass and orientation. We also show how to obta

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19

Vedenyapin, Victor Valentinovich, Nataliia Igorevna Karavaeva, Oksana Aleksandrovna Kostiuk, and Boris Nikolaevich Chetverushkin. "Schrödinger equation as a consequence of new Vlasov type equations." Keldysh Institute Preprints, no. 26 (2019): 1–11. http://dx.doi.org/10.20948/prepr-2019-26.

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20

Bendib, K., and A. Bendib. "Analytic solution of the Vlasov equation and closed fluid equations." Physics of Plasmas 6, no. 5 (1999): 1500–1507. http://dx.doi.org/10.1063/1.873402.

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21

Gasser, I., P. E. Jabin, and B. Perthame. "Regularity and propagation of moments in some nonlinear Vlasov systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 6 (2000): 1259–73. http://dx.doi.org/10.1017/s0308210500000676.

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We introduce a new variant to prove the regularity of solutions to transport equations of the Vlasov type. Our approach is mainly based on the proof of propagation of velocity moments, as in a previous paper by Lions and Perthame. We combine it with moment lemmas which assert that, locally in space, velocity moments can be gained from the kinetic equation itself. We apply our theory to two cases. First, to the Vlasov–Poisson system, and we solve a long-standing conjecture, namely the propagation of any moment larger than two. Next, to the Vlasov–Stokes system, where we prove the same result fo

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22

Kaneda, Takeshi, and Keishiro Niu. "Kinetic analysis of propagating ion beam with leading and trailing edges as ICF energy driver." Laser and Particle Beams 7, no. 2 (1989): 207–17. http://dx.doi.org/10.1017/s0263034600005978.

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Analysis is given for nonstationary propagation of rotating ion beam which has a finite length on the basis of Vlasov–Maxwell equations. The beam velocity distribution function is assumed to have a form of product of a modification function g which depends on time and axial coordinate multiplied by a steady solution fb0 which is a known function of particle velocity and radial coordinate. Unknown function g is solved as the solution of Vlasov equation through electromagnetic fields induced by leading and trailing edges. These electromagnetic fields can be solved from the Maxwell equations by u

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23

Bracken, Paul. "Equations with physical applications arising from the Vlasov chain." International Journal of Modern Physics B 34, no. 21 (2020): 2050207. http://dx.doi.org/10.1142/s0217979220502070.

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The first equation in a hierarchy of equations due to Vlasov is studied. The equation can be described as a Schrödinger equation for the probabilistic description of a system. It has applications in other areas as well. A physical meaning can be assigned to the phase of the wavefunction. The approach allows construction of solutions of the Schrödinger equation from known solutions and conversely much like a Bäcklund transformation. Finally, the process of introducing a potential into the Schrödinger equation is generalized to the case of Bohmian mechanics.

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24

Dragan, Vasile, and Samir Aberkane. "The Estimation of a Signal Generated by a Dynamical System Modeled by McKean–Vlasov Stochastic Differential Equations Under Sampled Measurements." Mathematics 13, no. 11 (2025): 1767. https://doi.org/10.3390/math13111767.

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This paper addresses the problem of optimal H2-filtering for a class of continuous-time linear McKean–Vlasov stochastic differential equations under sampled measurements. The main tool used to solve the filtering problem is a forward jump matrix linear differential equation with a Riccati-type jumping operator. More specifically, the stabilizing solution of such a jump Riccati-type equation plays a key role.

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25

BONILLA, LUIS L., and JUAN S. SOLER. "HIGH-FIELD LIMIT OF THE VLASOV–POISSON–FOKKER–PLANCK SYSTEM: A COMPARISON OF DIFFERENT PERTURBATION METHODS." Mathematical Models and Methods in Applied Sciences 11, no. 08 (2001): 1457–68. http://dx.doi.org/10.1142/s0218202501001410.

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A reduced drift-diffusion (Smoluchowski–Poisson) equation is found for the electric charge in the high-field limit of the Vlasov–Poisson–Fokker–Planck system, both in one and three dimensions. The corresponding electric field satisfies a Burgers equation. Three methods are compared in the one-dimensional case: Hilbert expansion, Chapman–Enskog procedure and closure of the hierarchy of equations for the moments of the probability density. Of these methods, only the Chapman–Enskog method is able to systematically yield reduced equations containing terms of different order.

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26

Besse, Nicolas, and Philippe Bechouche. "Regularity of weak solutions for the relativistic Vlasov–Maxwell system." Journal of Hyperbolic Differential Equations 15, no. 04 (2018): 693–719. http://dx.doi.org/10.1142/s0219891618500212.

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We investigate the regularity of weak solutions of the relativistic Vlasov–Maxwell system by using Fourier analysis and the smoothing effect of low velocity particles. This smoothing effect has been used by several authors (see Glassey and Strauss 1986; Klainerman and Staffilani, 2002) for proving existence and uniqueness of [Formula: see text]-regular solutions of the Vlasov–Maxwell system. This smoothing mechanism has also been used to study the regularity of solutions for a kinetic transport equation coupled with a wave equation (see Bouchut, Golse and Pallard 2004). Under the same assumpti

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27

Brahim, Hafida Ben, Hanane Ben Gherbal, and Boulakhras Gherbal. "A necessary conditions for optimal singular control of McKean-Vlasov stochastic differential equations driven by spatial parameters local martingale." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e5926. http://dx.doi.org/10.54021/seesv5n2-036.

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In this paper, we focus on stochastic singular control problems involving McKean-Vlasov stochastic differential equations driven by a spatially parameterized continuous local martingale. The drift coefficient in these equations depends on the state of the solution process and its law. The control variable consists of two components: an absolutely continuous control and a singular one. Firstly, under Lipschitz conditions, we establish the existence and uniqueness of its strong solution. Next, we derive the necessary conditions for optimal singular control under the assumption that the control d

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28

Tokarchuk, M. V. "Kinetic coefficients of ion transport in a porous medium based on the Enskog–Landau kinetic equation." Mathematical Modeling and Computing 11, no. 4 (2024): 1013–24. http://dx.doi.org/10.23939/mmc2024.04.1013.

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Normal solutions of the Enskog–Vlasov–Landau kinetic equation were obtained within the model of positively and negatively charged solid spheres for the system ion solution – porous medium. The Chapman–Enskog method was applied. Analytical expressions for coefficients of viscosity, thermal conductivity, diffusion of ions in the system ionic solution – porous medium were derived by constructing the equations of hydrodynamics on the basis of normal solutions of the kinetic equation.

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29

Sugaya, R. "Momentum-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma." Journal of Plasma Physics 56, no. 2 (1996): 193–207. http://dx.doi.org/10.1017/s0022377800019206.

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The momentum-space diffusion equation and the kinetic wave equation for resonant wave–wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov–Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave—wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation

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30

Yue, F., and Z. Y. Wu. "Iterative technique for a beam lying on a transversely isotropic foundation." Journal of Physics: Conference Series 2045, no. 1 (2021): 012004. http://dx.doi.org/10.1088/1742-6596/2045/1/012004.

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Abstract The effect of the foundation heterogeneity on the mechanical behaviour of a beam on Vlasov soils is discussed. According to a refined Vlasov soil model, the static problem of beams lying on transversely isotropic soils can be solved by an iterative method. In this paper, based on the energy variational principle, the differential equations for beams under an axial force on refined Vlasov foundations are derived. The methods for solving the internal forces and deformations of beams lying on refined elastic foundations are given. Additionally, an equation for the attenuation parameters

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31

CIARLET, PATRICK, and SIMON LABRUNIE. "NUMERICAL ANALYSIS OF THE GENERALIZED MAXWELL EQUATIONS (WITH AN ELLIPTIC CORRECTION) FOR CHARGED PARTICLE SIMULATIONS." Mathematical Models and Methods in Applied Sciences 19, no. 11 (2009): 1959–94. http://dx.doi.org/10.1142/s0218202509004017.

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When computing numerical solutions to the Vlasov–Maxwell equations, the source terms in Maxwell's equations usually fail to satisfy the continuity equation. Since this condition is required for the well-posedness of Maxwell's equations, it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. These approaches, which involve a hyperbolic, a parabolic and an elliptic correction, have been recently analyzed mathematically. The goal of this paper is to carry out the numerical analysis for several variants of Maxwell's equations with

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32

Yue, Feng, Fusheng Wang, Senqing Jia, Ziyan Wu, and Zhen Wang. "Bending Analysis of Circular Thin Plates Resting on Elastic Foundations Using Two Modified Vlasov Models." Mathematical Problems in Engineering 2020 (July 6, 2020): 1–12. http://dx.doi.org/10.1155/2020/2345347.

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The influence of soil heterogeneity is studied on the bending of circular thin plates using two modified Vlasov foundation models. The model parameters are determined reasonably using an iterative technique. According to the principle of minimum potential energy and considering transversely isotropic soils and Gibson soils, the governing differential equations and boundary conditions for circular thin plates on two modified Vlasov foundations are derived using a variational approach, respectively. The determination of attenuation parameters is a difficult problem, which has hindered the furthe

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33

Carrillo, José A., Young-Pil Choi, and Yingping Peng. "Large friction-high force fields limit for the nonlinear Vlasov–Poisson–Fokker–Planck system." Kinetic and Related Models 15, no. 3 (2022): 355. http://dx.doi.org/10.3934/krm.2021052.

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<p style='text-indent:20px;'>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 analys

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CHAE, MYEONGJU, KYUNGKEUN KANG, and JIHOON LEE. "GLOBAL CLASSICAL SOLUTIONS FOR A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL." Journal of Hyperbolic Differential Equations 10, no. 03 (2013): 537–62. http://dx.doi.org/10.1142/s0219891613500197.

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We consider a system coupling the compressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation on three-dimensional torus. The coupling arises from a drag force exerted by each other. We establish the existence of the global classical solutions close to an equilibrium, and further prove that the solutions converge to the equilibrium exponentially fast.

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35

Fimin, Nikolay Nikolaevich, and Valery Mihailovich Chechetkin. "Large–scale cosmological structures and Hammerstein–type equation for potential." Keldysh Institute Preprints, no. 79-e (2024): 1–18. https://doi.org/10.20948/prepr-2024-79-e.

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The criteria for the formation of stationary pseudo-periodic structures in a system of gravitating particles, described by the Vlasov–Poisson system of equations. Conditions studied branching solutions of a nonlinear integral equation for a generalized gravitational potential, leading to the emergence of coherent complex states of relative equilibrium in non-stationary systems of massive particles.

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36

Bao, Jianhai, Christoph Reisinger, Panpan Ren, and Wolfgang Stockinger. "First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (2021): 20200258. http://dx.doi.org/10.1098/rspa.2020.0258.

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In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order mom

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37

Frénod, Emmanuel, and Eric Sonnendrücker. "Homogenization of the Vlasov equation and of the Vlasov–Poisson system with a strong external magnetic field." Asymptotic Analysis 18, no. 3-4 (1998): 193–213. https://doi.org/10.3233/asy-1998-298.

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Motivated by the difficulty arising in the numerical simulation of the movement of charged particles in presence of a large external magnetic field, which adds an additional time scale and thus imposes to use a much smaller time step, we perform in this paper a homogenization of the Vlasov equation and the Vlasov–Poisson system which yield approximate equations describing the mean behavior of the particles. The convergence proof is based on the two‐scale convergence tools introduced by N’Guetseng and Allaire. We also consider the case where, in addition to the magnetic field, a large external

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38

Sugaya, Reiji. "Velocity-space diffusion due to resonant wave–wave scattering of electromagnetic and electrostatic waves in a plasma." Journal of Plasma Physics 45, no. 1 (1991): 103–13. http://dx.doi.org/10.1017/s002237780001552x.

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The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation.

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39

Hurst, Jérôme, Paul-Antoine Hervieux, and Giovanni Manfredi. "Phase-space methods for the spin dynamics in condensed matter systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2092 (2017): 20160199. http://dx.doi.org/10.1098/rsta.2016.0199.

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Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A

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40

Vedenyapin, Victor Valentinovich. "Vlasov-Maxwell-Einstein Equation." Keldysh Institute Preprints, no. 188 (2018): 1–20. http://dx.doi.org/10.20948/prepr-2018-188.

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Plácido, Hebe Q., and Ademir E. Santana. "Quantum generalized Vlasov equation." Physica A: Statistical Mechanics and its Applications 220, no. 3-4 (1995): 552–62. http://dx.doi.org/10.1016/0378-4371(95)00157-3.

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Santana, Ademir E., A. Matos Neto, and J. D. M. Vianna. "A generalized Vlasov equation." Physica A: Statistical Mechanics and its Applications 160, no. 3 (1989): 471–81. http://dx.doi.org/10.1016/0378-4371(89)90452-4.

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EROFEEV, V. I. "Derivation of an equation for three-wave interactions based on the Klimontovich–Dupree equation." Journal of Plasma Physics 57, no. 2 (1997): 273–98. http://dx.doi.org/10.1017/s0022377896004990.

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A collision integral for three-wave interactions in a collisionless plasma is derived from the full plasma description by means of the Klimontovich–Dupree and Maxwell equations. This collision integral differs from its traditional counterpart (calculated within the framework of Vlasov theory) by an additional functional factor. This means that the changes in the wave spectral density, which are induced by three-wave interactions, occur with a rate other than that calculated in Vlasov theory.

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Pilorz, Krzysztof. "A kinetic equation for repulsive coalescing random jumps in continuum." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 1 (2016): 47. http://dx.doi.org/10.17951/a.2016.70.1.47.

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A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to mesoscopic dynamics is performed by means of a Vlasov-type scaling. The existence and uniqueness of solutions of the corresponding kinetic equation are proved.

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Fimin, Nikolay Nikolaevich, and Valery Mihailovich Chechetkin. "Determinism of genesis of large-scale structures in astrophysics." Keldysh Institute Preprints, no. 67 (2023): 1–24. http://dx.doi.org/10.20948/prepr-2023-67.

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The criteria for the formation of non-stationary pseudo-periodic structures in a system of gravitating particles, described by the Vlasov--Poisson system of equations. Conditions of branching of solutions of a nonlinear integral equation for a generalized gravitational potential, leading to the emergence of coherent complex states of relative equilibrium in non-stationary systems of massive particles, is studied.

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46

Perepelkin, E. E., B. I. Sadovnikov, and N. G. Inozemtseva. "The properties of the first equation of the Vlasov chain of equations." Journal of Statistical Mechanics: Theory and Experiment 2015, no. 5 (2015): P05019. http://dx.doi.org/10.1088/1742-5468/2015/05/p05019.

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MELLET, A., and A. VASSEUR. "GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS." Mathematical Models and Methods in Applied Sciences 17, no. 07 (2007): 1039–63. http://dx.doi.org/10.1142/s0218202507002194.

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We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov–Fokker–Planck equation coupled to compressible Navier–Stokes equation via a drag force. The fluid is assumed to be barotropic with γ-pressure law (γ > 3/2). The existence of weak solutions is proved in a bounded domain of ℝ3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

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LI, QI, and CHE MING KO. "COVARIANT VLASOV EQUATION BASED ON THE WALECKA MODEL." Modern Physics Letters A 03, no. 05 (1988): 465–68. http://dx.doi.org/10.1142/s0217732388000556.

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We show that the relativistic Vlasov equation derived recently by us from the Walecka model under the local density and the classical approximations is equivalent to the covariant Vlasov equation derived by Elze et al. via the Wigner operator.

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Kassaw, Temesgen, and Gebretsadkan Woldemhret. "Relativistic Wave Propagation in Anisotropic Two-Component Magnetohydrodynamics Plasmas." Advances in Mathematical Physics 2022 (May 19, 2022): 1–11. http://dx.doi.org/10.1155/2022/9692145.

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This paper investigates the instabilities and characteristics of relativistic linear waves of two-component plasma by assuming the plasma to be in-viscid, homogeneous, collision-less, and magnetized. To do this, by taking moments of the relativistic Vlasov equation, the basic equations of the two-component relativistic an-isotropic plasma are derived. The linearized equations are analyzed for small perturbation under the assumption of the plasma which is initially at rest. After we derived the dispersion relations, different wave modes and instabilities are discussed analytically and numerical

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Tokarchuk, M. V. "Kinetic description of ion transport in the system "ionic solution – porous environment"." Mathematical Modeling and Computing 9, no. 3 (2022): 719–33. http://dx.doi.org/10.23939/mmc2022.03.719.

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A kinetic approach based on a modified chain of BBGKI equations for nonequilibrium particle distribution functions was used to describe the ion transfer processes in the ionic solution – porous medium system. A generalized kinetic equation of the revised Enskog–Vlasov–Landau theory for the nonequilibrium ion distribution function in the model of charged solid spheres is obtained, taking into account attractive short-range interactions for the ionic solution – porous medium system.

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