Large time behavior for the non-isentropic Navier-Stokes-Maxwell system

TL;DR

This paper proves the global existence and analyzes the large-time decay behavior of solutions to the non-isentropic Navier-Stokes-Maxwell system in three dimensions, improving previous decay rate results.

Contribution

It establishes global solutions near steady states and refines decay rate estimates for the coupled system using linearized analysis.

Findings

Global existence of solutions near steady states

Derived decay rates for perturbed solutions

Improved decay estimates over previous results

Abstract

In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time-decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on the linearized analysis of the non-isentropic Navier-Stokes-Poisson equations and the electromagnetic part for the linearized isentropic Navier-Stokes-Maxwell equations. In the meantime, the time-decay rates obtained by Zhang, Li, and Zhu~[{\it J. Differential Equations, 250(2011), 866-891}] for the linearized non-isentropic Navier-Stokes-Poisson equations are improved.