Abstract
The initial boundary value problem for a compressible Euler system out-side a ball in R3 is considered in this paper.Assuming the initial data have small and compact supported perturbations near a constant state,we show that the solution will blow up in a finite time,and the lifespan estimate can be estimated by the small pa-rameter of the initial perturbations.To this end,a"tricky"test function admitting good behavior is introduced.
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