Local existence and uniqueness of the mild solution to the 1D Vlasov–Poisson system with an initial condition of bounded variation |
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| Authors: | Simon Labrunie Sandrine Marchal Jean‐Rodolphe Roche |
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| Affiliation: | Institut élie Cartan (Mathématiques) UMR 7502, Nancy‐Université, CNRS and INRIA (project CALVI), 54056 Vand?uvre‐lès‐Nancy cedex, France |
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| Abstract: | 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 W1,1(?2), then we extend it to initial conditions lying in the space BV(?2), without any assumption of continuity, boundedness or compact support. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | Vlasov– Poisson system bounded variation functions Banach contraction mapping principle |
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