Uniform bounds and exponential time decay results for the Vlasov-Poisson-Fokker-Planck system
Résumé
We consider the non-linear VPFP system with a coulombian repulsive interaction potential and a generic confining potential in space dimension $d \geq 3$. Using spectral and kinetic methods we prove existence and uniqueness of a mild solution in weighted spaces and for small charge we find an explicit exponential rate of convergence toward the equilibrium in terms of the Witten Laplacian associated to the linear equation.