Long time existence of smooth solutions to 3D Euler-Poisson system of electrons with non-zero vorticity

In this paper, we investigate the long-term stability of classical solution to 3D one-fluid Euler-Poisson system of electrons with non-zero vorticity. It is shown that the classical solution is well-posed for a lifesapn Tδ at least εδ, where ε> 0 is the size of the initial perturbed density and velocity, δ> 0 is the size of the initial vorticity. This implies that the lifespan Tδ only essentially depends on the size δ of the initial vorticity.