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 $T_{\delta }$ at least $\frac{\epsilon }{\delta }$, where $\epsilon >0$ is the size of the initial perturbed density and velocity, $\delta >0$ is the size of the initial vorticity. This implies that the lifespan $T_{\delta }$ only essentially depends on the size $\delta$ of the initial vorticity.