Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge

Boundary Value Problems for the Stationary Vlasov-Boltzmann-Poisson Equation

We investigate the well posedness of stationary Vlasov-Boltzmann equations both in the simpler case of linear problem with a space varying force field and a collisional integral satisfying the detailed balanced principle with a non-singular scattering function, and, the non-linear Vlasov-Poisson-Boltzmann system. For the former we obtain existence-uniqueness results for arbitrarily large integr...

Poisson bracket for the Vlasov equation on a symplectic leaf

It is by now well known that many nondissipative continuous systems possess a Hamiltonian structure, which when viewed in terms of Eulerian variables has a noncanonical form. Examples from plasma physics include ideal magnetohydrodynamics (MHD) [1], theVlasovequation [2], the two-fluid equations [3], and the BBGKY hierarchy [4]. A common feature of all these systems is that they possess Casimir...

Streamline diffusion methods for the Vlasov-Poisson equation

— We prove error estimâtes for the streamline diffusion and the discontinuous Galerkin finite element methods for discretization of the Vlasov-Poisson équation. Résumé. — Nous démontrons des estimations d'erreur pour la méthode de Galerkin discontinue pour la discrétisation de l'équation de Vlasov-Poisson.

From Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck Systems to Incompressible Euler Equations: the case with finite charge

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 bounde...

Some remarks on a stationary Vlasov-Poisson system with source term arising in ion beam neutralization