Vlasov–Poisson system

Summary

The Vlasov–Poisson system is the Vlasov equation in which the force is the gradient of a potential. The potential solves Poisson's equation with the particle density as source. It describes a large collection of particles that interact only through their common electric or gravitational field, with collisions neglected. With a repulsive force it models a plasma of electrons, and with an attractive force it models stars in a galaxy. It is a basic nonlinear kinetic equation, with conserved mass and energy, and with phenomena such as Landau damping.