Local Existence and Uniqueness of a Mild Solution to the One Dimensional Vlasov-Poisson System with an Initial Condition of Bounded Variation

Simon Labrunie (1, 2) , Sandrine Marchal (1, 2) , Jean Rodolphe Roche (1, 2)

1 CALVI - Scientific computation and visualization
2 IECN - Institut Élie Cartan de Nancy

We propose a result of local existence and uniqueness of a mild solution to the one-dimensional Vlasov-Poisson system. We establish the result for an initial condition lying in the Sobolev space of integrable functions with integrable derivatives, then we extend it to initial conditions lying in the space of functions of bounded variation, without any assumption of continuity, boundedness or compact support.

Mots clés: Vlasov-Poisson system; bounded variation functions; Banach contraction mapping principle

Domaines: Equations aux dérivées partielles [math.AP]

Simon Labrunie, Sandrine Marchal, Jean Rodolphe Roche. Local Existence and Uniqueness of a Mild Solution to the One Dimensional Vlasov-Poisson System with an Initial Condition of Bounded Variation. [Research Report] RR-6946, INRIA. 2009, pp.14. ⟨inria-00389829⟩