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

Research output: Contribution to journalArticleResearchpeer-review

18 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 languageEnglish
Pages (from-to)1141-1167
Number of pages27
JournalCommunications in Partial Differential Equations
Volume30
Issue number7-9
DOIs
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Incompressible Euler equations
  • Optimal transportation
  • Quasineutral limit

Cite this

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abstract = "This paper studies the pressureless Euler-Poisson system and its fully nonlinear counterpart, the Euler-Monge-Amp{\`e}re system, where the fully nonlinear Monge-Amp{\`e}re 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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}

Quasi-neutral limit of the Euler-Poisson and Euler-Monge-Ampère systems. / Loeper, Grégoire.

In: Communications in Partial Differential Equations, Vol. 30, No. 7-9, 2005, p. 1141-1167.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Loeper, Grégoire

PY - 2005

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N2 - 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.

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.

KW - Incompressible Euler equations

KW - Optimal transportation

KW - Quasineutral limit

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JF - Communications in Partial Differential Equations

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