Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)
SujetKinetic equations; Fokker-Planck equation; Vlasov equation; Poisson equation; Poisson-Boltzmann-Emden equation; Confinement; Stationary solutions; Long time asymptotics; Steady states; Renormalized solutions; A priori estimates; Entropy; Free energy; Configurational free energy; Jensen's inequality; Marcinkiewicz spaces; Semilinear elliptic equations
Journal issueJournal de mathématiques pures et appliquées
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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.
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