Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 58, pp. 1-11.

Title: On global solutions for the Vlasov-Poisson system

Author: Peter Zhidkov (Joint Institute for Nuclear Research, Dubna, Russia)

Abstract: 
 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.