Large time behavior of the full compressible Navier-Stokes-Maxwell system with a nonconstant background density

We study the Cauchy problem for the full compressible Navier-Stokes-Maxwell system with a nonconstant background density in $R^3$. By means of suitable choosing of symmetrizers and weighted energy estimates with some new developments, we establish the global existence and uniqueness of the classical solution provided that the initial data are near this equilibrium. Furthermore, by using the spectrum analysis on the linearized homogeneous system of the full compressible Navier-Stokes-Maxwell equations and refining the convergence property, we obtain the time-algebraic convergence rates of the perturbed solutions.