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.
- Incompressible Euler equations
- Optimal transportation
- Quasineutral limit