On the attractive plasma-charge system in 2-d
  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. 
Silvia Caprino, Carlo Marchioro, Evelyne Miot, Mario Pulvirenti
math.AP