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Quasineutral limit for Vlasov-Poisson with Penrose stable data. (Limite quasi neutre pour Vlasov-Poisson avec des données stables au sens de Penrose.) (English. French summary) Zbl 1361.35179

The purpose of this paper is to study a Vlasov-Poisson system for ions in a plasma, where the unknown function is a distribution in the phase space. The main theorem states that this system has a unique solution for stable Penrose initial data. The limit equation for these data is also studied.
For the proof appropriate differential operators, which fit together with the Vlasov equation, are introduced. The proofs consist of many steps and use Leibniz and Taylor formulas, Sobolev embedding theorem, Sobolev-Gagliardo-Nirenberg-Moser, Gronvall, Cauchy-Schwartz, Bessel inequalities, Fourier transform.

MSC:

35Q83 Vlasov equations
35Q35 PDEs in connection with fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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