The Asymptotic Behavior of Globally Smooth Solutions of Bipolar Nonisentropic Compressible Euler--Maxwell System for Plasma

Abstract

The bipolar nonisentropic compressible Euler--Maxwell system is investigated in $R^3$ in the present paper, and the $L^n$ time decay rate for the global smooth solution is established. It is shown that the total densities, total temperatures, and magnetic field of two carriers converge to the equilibrium states at the same rate $(1+t)^{-\frac{3}{2}+\frac{3}{2n}}$ in $L^n$ norm. But both the difference of densities and the difference of temperatures of two carriers decay at the rate $(1+t)^{-2-\frac{1}{n}}$, and the velocity and electric field decay at the rate $(1+t)^{-\frac{3}{2}+\frac{1}{2n}}$. This phenomenon on the charge transport shows the essential difference between the nonisentropic unipolar Euler--Maxwell and the bipolar isentropic Euler--Maxwell system.