# Stability of non-constant equilibrium solutions for two-fluid non-isentropic Euler-Maxwell systems arising in plasmas

## TL;DR

This paper proves the global stability of non-constant equilibrium solutions in two-fluid non-isentropic Euler-Maxwell plasma models, extending previous results by employing new symmetrization techniques and energy estimates.

## Contribution

It introduces a novel approach using symmetrizers and induction on derivatives to establish stability without temperature diffusion terms.

## Key findings

- Established global smooth solutions near non-constant equilibria
- Demonstrated asymptotic stability of solutions
- Extended previous models by replacing densities with pressure functions

## Abstract

We consider the periodic problem for two-fluid non-isentropic Euler-Maxwell systems in plasmas. By means of suitable choices of symmetrizers and an induction argument on the order of the time-space derivatives of solutions in energy estimates, the global smooth solution with small amplitude is established near a non-constant equilibrium solution with asymptotic stability properties. This improves the results obtained in \cite{LWF16a} for models with temperature diffusion terms by using the pressure functions $p^\nu$ in place of the unknown variables densities $n^\nu$.