The asymptotic behavior of globally smooth solutions of bipolar non-isentropic compressible Euler-Maxwell system for plasma

TL;DR

This paper analyzes the long-term decay rates of smooth solutions to the bipolar non-isentropic compressible Euler-Maxwell system in three dimensions, revealing how different physical quantities approach equilibrium over time.

Contribution

It establishes the $L^q$ decay rates for various physical quantities in the bipolar non-isentropic Euler-Maxwell system, highlighting differences from the unipolar case.

Findings

Total densities, temperatures, and magnetic field decay at rate $(1+t)^{-3/2+3q/2}$.

Differences in densities and temperatures decay at rate $(1+t)^{-2-1/q}$.

Velocity and electric field decay at rate $(1+t)^{-3/2+1/(2q)}$.

Abstract

The bipolar non-isentropic compressible Euler-Maxwell system is investigated in $R^3$ in the present paper, and the $L^q$ 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 $(1+t)^{-3/2+3q/2}$ in $L^q$ norm. But, both the difference of densities and the difference of temperatures of two carriers decay at the rate $(1+t)^{-2-\frac{1}{q}}$, and the velocity and electric field decay at the rate $(1+t)^{-3/2+\frac{1}{2q}}$. This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar Euler-Maxwell and the bipolar isentropic Euler-Maxwell system.