Global weak solutions to the cometary flow equation with a self-generated electric field

Abstract

We study the Cauchy problem of a cometary flow equation with a self-generated electric field. This kinetic model originates from the theory of astrophysical plasmas and can be viewed as a perturbation, by a wave-particle collision operator, of the classical Vlasov–Poisson system. By asymptotic methods in kinetic theory, global existence of nonnegative weak solutions to the Cauchy problem in three space variables is established for bounded initial data having finite second order velocity moments.