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In this paper, we consider the quasineutral limit of the Euler-Poissonequation for a clod, ion-acoustic plasma when the Debye length tends to zero.When the ion-acoustic plasma is cold, the Euler-Poisson equation ispressureless and hence fails to be Friedrich symmetrisable, which excludes theapplication of the classical energy estimates method. This brings newdifficulties in proving uniform estimates independent of $\varepsilon$. Themain novelty in this article is to introduce new $\varepsilon$-weighted normsof the unknowns and to combine energy estimates in different levels withweights depending on $\varepsilon$. Finally, that the quasineutral regimes arethe incompressible Euler equations is proven for well prepared initial data.

Quasineutral limit of the Euler-Poisson equation for a cold, ion-acoustic plasma