Long Time Existence of Smooth Solutions to 3D Euler–Poisson System of Electrons With Nonzero Vorticity

Abstract

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