Blow-up for compressible Euler system with space-dependent damping in 1-D

Abstract This article considers the Cauchy problem for compressible Euler system in R {\bf{R}} with damping, which coefficient depends on space variable. Assuming initial density has a small perturbation around constant state and both velocity field are compact supported, finite-time blow-up result will be established. reveals fact that if space-dependent damping decays fast enough far (belongs to L 1 ( ) {L}^{1}\left({\bf{R}}) ), then is non-effective long-time behavior of solution.