In this talk I will consider a two-dimensional system in which some negatively charged particles are immersed in a sea of positively charged light particles (plasma). In terms of a mean-field approximation, the evolution is conveniently described by a Vlasov-Poisson type equation for the plasma density with an extra singular field created by the charged particles. I will present a global existence result of a solution under suitable assumptions on the support of the plasma density. Uniqueness remains unsolved. This is joint work with Silvia Caprino, Carlo Marchioro and Mario Pulvirenti.

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