The suppressible property of the solution for three-dimensional Euler equations with damping

We consider the concentration of the energy for three-dimensional compressible Euler equations with damping. By using certain weighted estimates, it is proved that the damping suppresses the support of the solution in the sense that the solution decays exponentially outside of the set |x|⩽t(1/2)+δ|x|⩽t(1/2)+δ for δ>0δ>0. Formation of singularities is also exhibited for large date.