On classical solutions of the two-species Vlasov–Poisson system in R3 with infinite charge

Abstract

We are concerned with the initial value problem for the two-species Vlasov–Poisson system in the plasma physics case in R3. It is assumed that initially the phase-space densities of ions and electrons decay only polynomially with respect to the velocities, but the net charge density vanishes at infinity with a polynomial rate, which allows for defining the electrostatic field. This situation falls into the so-called infinite charge problem, and there is no rigorous result as far as we know. Local existence, uniqueness, and continuation criteria of the classical solution are established in this paper. Moreover, this article also shows the existence of a global solution in the case of radial symmetry.