Global existence and asymptotic decay of solutions to the Non-isentropic   Euler-Maxwell system
  The non-isentropic compressible Euler-Maxwell system is investigated in $R^3$ in the present paper, and the $L^q$ time decay rate for the global smooth solution is established. It is shown that the density and temperature of electron converge to the equilibrium states at the same rate $(1+t)^{-11/4}$ in $L^q$ norm. 
Yuehong Feng, Shu Wang and Shuichi Kawashima
math.AP