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

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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
Issue number7-9
Publication statusPublished - 2005
Externally publishedYes


  • Incompressible Euler equations
  • Optimal transportation
  • Quasineutral limit

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