Time evolution of a Vlasov–Poisson plasma with different species and infinite mass in $${\mathbb {R}}^3$$R3

We study existence and uniqueness of the solution to the Vlasov–Poisson system describing a plasma constituted by different species evolving in $${\mathbb {R}}^3$$, whose particles interact via the Coulomb potential. The species can have both positive or negative charge. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law, extending a result contained in Caprino et al. (J Stat Phys 169:1066–1097,2017), which was restricted to finite total mass.