Asymptotic behavior of the compressible non-isentropic Navier-Stokes-Maxwell system in $\mathbb{R}^3$

Abstract

The compressible non-isentropic Navier-Stokes-Maxwell system is investigated in $\mathbb{R}^3$ and the global existence and large time behavior of solutions are established by pure energy method provided the initial perturbation around a constant state is small enough. We first construct the global unique solution under the assumption that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If further the initial data belongs to $\dot{H}^{-s}$ ($0≤ s<3/2$) or $\dot{B}_{2,∞}^{-s}$ ($0< s≤3/2$), by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the $L^p$-$L^2$ $(1≤ p≤ 2)$ type of the decay rates follows without requiring that the $L^p$ norm of initial data is small.