# Quasineutral limit for the Vlasov Poisson system

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Frederic Rousset , Universite Paris-Sud, Orsay
Fine Hall 322

We shall study  the quasi-neutral limit of the Vlasov-Poisson system. This is a very singular limit   due to the presence of the two streams instability in plasmas. In particular the convergence towards the expected limit system cannot be always true in Sobolev spaces.  We will justify this limit and prove the well-posedness of the limit system for initial data in Sobolev spaces for which the profile in the velocity variable  satisfies some linear  stability condition. (joint work with D. Han-Kwan)