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An introduction to the Vlasov-Poisson system (and to its quasineutral limit)

The Vlasov-Poisson system is a classical PDE model of plasma physics, used to describe the dynamics in phase space of interacting charged particles. We will review some remarkable mathematical properties of this system. The topics reviewed should include (1) the existence of weak or strong solutions, (2) the stability and instability theory of certain equilibria, (3) the quasineutral limit, i.e. the regime when the Debye length is small compared to the typical observation length.

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