Abstract. We prove uniqueness for the vortex-wave system with a single point vortex introduced by Marchioro and Pulvirenti [7] in the case where the vorticity is initially constant near the point vortex. Our method relies on the Eulerian approach for this problem and in particular on the formulation in terms of the velocity.
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov-Poisson system in presence of point charges in case of repulsive interaction. The present analysis extends an analogeous two-dimensional result [1].
We study a positively charged Vlasov-Poisson plasma in which N negative point charges are immersed. The attractiveness of the system forces us to consider a possibly unbounded plasma density near the charges. We prove the existence of a global in time solution, assuming a suitable initial distribution of the velocities of the plasma particles. Uniqueness remains unsolved
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