## Abstract

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 e ects. 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.

Original language | English (US) |
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Pages (from-to) | 247-296 |

Number of pages | 50 |

Journal | Journal de l'Ecole Polytechnique - Mathematiques |

Volume | 2 |

DOIs | |

State | Published - 2015 |

## Keywords

- Incompressible Euler equations
- Lake equations
- Modulated energy
- Plasma physics
- Quasi–neutral regime
- Relative entropy
- Vlasov–Poisson system
- Vlasov–Poisson–Fokker–Planck system

## ASJC Scopus subject areas

- Mathematics(all)