Local existence and uniqueness of the mild solution to the 1D Vlasov--Poisson system with an initial condition of bounded variation

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

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

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 space $W^{1,1}(\mathbb{R}^2)$, then we extend it to initial conditions lying in the space $BV(\mathbb{R}^2)$, 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 the mild solution to the 1D Vlasov--Poisson system with an initial condition of bounded variation. 2009. ⟨hal-00397497v1⟩