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

Mario Pulvirenti (1) , Chiara Simeoni (2)

1 Mathematical Physics
2 PDEs and Numerical Analysis

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

Domaines: Physique mathématique [math-ph]

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)23:10<923::AID-MMA143>3.0.CO;2-R⟩. ⟨hal-00905933v1⟩