Abstract
AbstractThis article considers the Cauchy problem for compressible Euler system inR{\bf{R}}with damping, in which the coefficient depends on the space variable. Assuming the initial density has a small perturbation around a constant state and both the small perturbation and the small initial velocity field are compact supported, finite-time blow-up result will be established. This result reveals the fact that if the space-dependent damping coefficient decays fast enough in the far field (belongs toL1(R){L}^{1}\left({\bf{R}})), then the damping is non-effective to the long-time behavior of the solution.
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