A RIGOROUS STABILITY RESULT FOR THE VLASOV-POISSON SYSTEM IN 3 DIMENSIONS

It is proven that in a neutral two-component plasma with space homogeneous positively charged background, which is governed by the Vlasov-Poisson system and for which Poisson's equation is considered on a cube in R3 with periodic boundary conditions, the space homogeneous stationary solutions g with energy gradient partial derivative g/partial derivative epsilon less-than-or-equal-to 0 and compact support are (nonlinearly) stable in the L1-norm with respect to weak solutions of the initial value problem.