From Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck Systems to Incompressible Euler Equations: the case with finite charge

Julien Barré (1) , David Chiron (1) , Thierry Goudon (1, 2) , Nader Masmoudi (3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment
3 CIMS - Courant Institute of Mathematical Sciences [New York]

We study the asymptotic regime of strong electric fields that leads from the Vlasov–Poisson system to the Incompressible Euler equations. We also deal with the Vlasov–Poisson–Fokker– Planck system which induces dissipative effects. The originality consists in considering a situation with a finite total charge confined by a strong external field. In turn, the limiting equation is set in a bounded domain, the shape of which is determined by the external confining potential. The analysis extends to the situation where the limiting density is non–homogeneous and where the Euler equation is replaced by the Lake Equation, also called Anelastic Equation.

Domaines: Mathématiques [math]

Julien Barré, David Chiron, Thierry Goudon, Nader Masmoudi. From Vlasov–Poisson and Vlasov–Poisson–Fokker–Planck Systems to Incompressible Euler Equations: the case with finite charge. Journal de l'École polytechnique — Mathématiques, 2015, pp.247-296. ⟨10.5802/jep.24⟩. ⟨hal-01121534⟩