Decay estimates of solutions to the compressible Euler-Maxwell system in R3

We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\mathring{3}$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If the initial data belongs to $\text{Dot}{H}^{-s}$ ($0\le s<3\mathrm{/}2$) or ${\dot{B}}_{2,\mathrm{\infty }}^{-s}$ ($0<s\le 3\mathrm{/}2$), by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the usual $L^p$–$L^2$ $(1\le p\le 2)$ type of the decay rates follow without requiring that the $L^p$ norm of initial data is small.