Long‐term stability of periodic smooth irrotational flows to the electrons Euler–Poisson system in three dimensions

Abstract

We are concerned with the one‐fluid Euler–Poisson system for the electrons on the cubes in three dimensions. With the bootstrap estimates, we prove long‐term stability of periodic solutions of this system with small smooth irrotational perturbations of a constant background. Our main result is that the solutions are well‐posed for a time at least , where is the size of the initial data, the sufficiently large is the side length of the cubes, and is the index of the classical Sobolev spaces .