The Vlasov‐Poisson‐Boltzmann system near Maxwellians

The dynamics of dilute electrons can be modeled by the Vlasov‐Poisson‐Boltz‐mann system, where electrons interact with themselves through collisions and with their self‐consistent electric field. It is shown that any smooth, periodic initial perturbation of a given global Maxwellian that preserves the same mass, momentum, and total energy (including both kinetic and electric energy), leads to a unique global‐in‐time classical solution. The construction of global solutions is based on an energy method with a new estimate of dissipation from the collision: ∫₀^t〈Lf(s), f(s)〉ds is positive definite for solution f(t,x,v) with small amplitude to the Vlasov‐Poisson‐Boltzmann system (1.4). © 2002 Wiley Periodicals, Inc.