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 (R 2 ), then we extend it to initial conditions lying in the space BV(R 2 ), without any assumption of cont
✦ LIBER ✦
Uniqueness of the solution to the Vlasov–Poisson system with bounded density
✍ Scribed by Grégoire Loeper
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 152 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0021-7824
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## Abstract A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. A fixed background of positive charge, dependent only upon velocity, is assumed and the situation in which the mobile negative ions balance the positive charge as |__x__| → ∞ is considered. Thus, the total