Abstract (EN)

This paper is devoted to the characterization of external electrostatic potentials for which the Vlasov-Poisson-Fokker-Planck system satisfies one of the following properties: (i) the system admits stationary solutions, (ii) any solution to the evolution problem converges to a stationary solution, or, equivalently, no mass vanishes for large times, (iii) the free energy is bounded from below, We give conditions under which these different notions of confinement are equivalent.