Large time behavior of solutions for compressible Euler equations with damping in R3

We consider the long-time behavior and optimal decay rates of global strong solutions for the isentropic compressible Euler equations with damping in R3 in the present paper. When the regular initial data belong to some Sobolev space with l⩾4 and s∈[0,1], we show that the density of the system converges to its equilibrium state at the rates in the L2-norm or in the L∞-norm respectively; the momentum of the system decays at the rates in the L2-norm or in the L∞-norm respectively, which are shown to be optimal for the compressible Euler equations with damping.