We consider the Vlasov–Poisson equation in R3 with initial data which are not L1 in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we prove the existence and uniqueness of the solution, thus generalizing the analogous result by the same authors for data compactly supported in the velocities.
We study existence and uniqueness of the solution to the Vlasov–Poisson system describing a plasma constituted by different species evolving in R3, 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.
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