Variational formulations for Vlasov–Poisson–Fokker–Planck systems

Abstract

Time-discrete variational schemes are introduced for both the Vlasov–Poisson–Fokker–Planck (VPFP) system and a natural regularization of the VPFP system. The time step in these variational schemes is governed by a certain Kantorovich functional (or scaled Wasserstein metric). The discrete variational schemes may be regarded as discretized versions of a gradient flow, or steepest descent, of the underlying free energy functionals for these systems. For the regularized VPFP system, convergence of the variational scheme is rigorously established. Copyright © 2000 John Wiley & Sons, Ltd.