$L^{\infty}$-estimates for the Vlasov-Poisson-Fokker-Planck equation

Mario Pulvirenti (1) , Chiara Simeoni (1)

1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]

We consider the Vlasov-Poisson-Fokker-Planck equation, in three dimensions, as the backward Kolmogorov equation associated with a nonlinear diffusion process. In this way, we derive new $L^{\infty}$-estimates on the spatial density, which are uniform in the diffusion parameters.

Mots clés: nonlinear diffusion processes; uniform energy estimates; stochastic calculus; singular potential field; plasma dynamics

Domaines: Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Mario Pulvirenti, Chiara Simeoni. $L^{\infty}$-estimates for the Vlasov-Poisson-Fokker-Planck equation. Mathematical Methods in the Applied Sciences, 2000, 23 (10), pp.923-935. ⟨10.1002/1099-1476(20000710)23:103.0.CO;2-R⟩. ⟨hal-00905933v2⟩