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