Electron. J. Diff. Eqns., Vol. 2004(2004), No. 58, pp. 1-11.

On global solutions for the Vlasov-Poisson system

Peter Zhidkov

In this article we show that the Vlasov-Poisson system has a unique weak solution in the space $L_1\cap L_\infty$. For this purpose, we use the method of characteristics, unlike the approach in [12].

Submitted February 13, 2004. Published April 14, 2004.
Math Subject Classifications: 35Q72, 82C05, 82C40.
Key Words: Vlasov equation, initial value problem, global weak solution, Coulomb potential of interactions, existence and uniqueness of a solution.

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Peter E. Zhidkov
Bogoliubov Laboratory of Theoretical Physics,
Joint Institute for Nuclear Research,
141980 Dubna (Moscow region), Russia
e-mail: zhidkov@thsun1.jinr.ru
Fax: 7-(09621-)65084

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