Blowup phenomena for the N-dimensional compressible Euler equations with damping

In this paper, we extend the finite propagation speed property for the compressible Euler equations with damping from the three-dimensional case to the general N-dimensional case. Subsequently, blowup results of the N-dimensional compressible Euler equations with damping are obtained. More precisely, we show that if the initial data 0∫∞f(r)V(0,r)dr are sufficiently large, then blowup phenomena occurs and the finite blowup time can be estimated, where f is a general test function with mild conditions and V represents the speed of the fluid in radial symmetry. Copyright © 2017 Springer International Publishing.