In this paper,we consider the long-time behavior of the initial boundary value problem of the com-pressible Euler system in the exterior domain in high dimensions(n=2,3).Assuming the initial density and velocity admit small compactly supported perturbations near constant states,we show finite-time blow-up of the initial boundary value problem with the impermeable boundary condition.The upper bound of the lifespan estimate with respect to the small parameter of the initial perturbations is given.To this end,a test function method is introduced,which seems quite simple.The energy equality is also involved.
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