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The initial boundary value problem for a compressible Euler system outside a ball in $\mathbf{R}^3$ 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 parameter of the initial perturbations. To this end, a “tricky” test function admitting good behavior is introduced.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n2.24.06}, url = {http://global-sci.org/intro/article_detail/jms/23170.html} }The initial boundary value problem for a compressible Euler system outside a ball in $\mathbf{R}^3$ 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 parameter of the initial perturbations. To this end, a “tricky” test function admitting good behavior is introduced.