Propagation of space moments in the Vlasov-Poisson Equation and further results

We show that, if the initial data has moments in the space variable x highe r than three, then the corresponding solution f(t, x, v) of the Vlasov-Pois son System has also moments in x - vt higher than three (propagation of hig h space moments). We also prove the propagation of low moments in the space or in the velocity variable, and state further a priori estimates for solu tions of the Vlasov-Poisson System having infinite kinetic energy. (C) Else vier, Paris.