  This paper studies the pressureless Euler-Poisson system and its fully
non-linear counterpart, the Euler-Monge-Amp\`ere system, where the fully
non-linear Monge-Amp\`ere 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.
