Related papers: Decay in Time for a One-Dimensional Two-Component …
For a class of arbitrary large initial data with radial symmetry or cylindrical symmetry, we prove the existence of global solutions for the $3D$ relativistic Vlasov-Poisson system for the plasma physics case. The compact support assumption…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…
The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects…
A phenomenological model using fluid theory is developed to show that the decay of two seemingly independent nonlinear structures namely the dust void and dust soliton strongly depends on the plasma ionization parameter in an unmagnetized…
A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this…
Motion of massive and massless test particle in equilibrium and non-equilibrium case is discussed in a dyadosphere geometry through Hamilton-Jacobi method. Geodesics of particles are discussed through Lagrangian method too. Scalar wave…
The collision operator for a relativistic plasma is reformulated in terms of an expansion in spherical harmonics. In this formulation the collision operator is expressed in terms of five scalar potentials which are given by one-dimensional…
We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the…
We review stability and instability results for self-gravitating matter distributions, where the matter model is a collisionless gas as described by the Vlasov equation. The focus is on the general relativistic situation, i.e., on steady…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of…
We consider the classical and relativistic Vlasov-Poisson systems with spherically-symmetric initial data and prove the optimal decay rates for all suitable $L^p$ norms of the charge density and electric field, as well as, the optimal…
We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…
We develop a method for investigating the relationship between the shape of a 1-particle distribution and non-linear electrostatic oscillations in a collisionless plasma, incorporating transverse thermal motion. A general expression is…
A new splitting is proposed for solving the Vlasov-Maxwell system. This splitting is based on a decomposition of the Hamiltonian of the Vlasov-Maxwell system and allows for the construction of arbitrary high order methods by composition…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
We perform a numerical study of the critical regime for the general relativistic collapse of collisionless matter in spherical symmetry. The evolution of the matter is given by the Vlasov equation (or Boltzmann equation) and the geometry by…
We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. In particular, we construct solutions that initially possess arbitrarily small charge…
We construct a mean-field model that describes the nonlinear dynamics of a spin-polarized electron gas interacting with fixed, positively-charged ions possessing a magnetic moment that evolves in time. The mobile electrons are modeled by a…
In this paper, we derive a Vlasov type kinetic model for diatomic plasma in which each ion consists of two atoms bonded through an oscillatory intermolecular force given by a singular Hooke potential. We then consider the existence and…