Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems

Grégoire Loeper

doi:10.1080/03605300500257545

Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems

Grégoire Loeper

Research output: Contribution to journal › Article › Research › peer-review

20 Citations (Scopus)

Abstract

This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.

Original language	English
Pages (from-to)	1141-1167
Number of pages	27
Journal	Communications in Partial Differential Equations
Volume	30
Issue number	7-9
DOIs	https://doi.org/10.1080/03605300500257545
Publication status	Published - 2005
Externally published	Yes

Keywords

Incompressible Euler equations
Optimal transportation
Quasineutral limit

Access to Document

10.1080/03605300500257545

Link to publication in Scopus

Cite this

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AB - This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Ampère system, where the fully nonlinear Monge-Ampère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometric approximation to the Euler incompressible equations. Using energy estimates, convergence of both systems to the Euler incompressible equations is proved.

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KW - Quasineutral limit

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