Local existence for the one-dimensional Vlasov-Poisson system with infinite mass

A collisionless plasma is modelled by the Vlasov-Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as [x] (right arrow)(infinity). Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established.