A rigorous stability result for the Vlasov-Poisson system in three dimensions
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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 inR3 with periodic boundary conditions, the space homogeneous stationary solutions g with energy gradient ∂g/∂ε ≤ 0 and compact support are (nonlinearly) stable in the L1-norm with respect to weak solutions of the initial value problem.
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