In this talk, I will focus on a fundamental model in plasma physics, namely the Euler-Poisson system, posed on the torus. This equation describes teh flow of an incompressible fluid of electrons under its own electrostatic force. I will show the long term regularity of the Euler-Poisson system on 2D tori. The conclusion is that, if the initial data is epsilon close to the constant solution, then the life span of the solution is at least R/\epsilon^2(log R)^{O(1)}. Time permitting, I will also talk about similar results in 3D periodic water waves.