TY - JOUR
T1 - Formation of Singularity for Compressible Euler Equations Outside a Ball in 3-D
AU - Li , Mengxuan
AU - Geng , Jinbo
JO - Journal of Mathematical Study
VL - 2
SP - 223
EP - 229
PY - 2024
DA - 2024/06
SN - 57
DO - http://doi.org/10.4208/jms.v57n2.24.06
UR - https://global-sci.org/intro/article_detail/jms/23170.html
KW - Compressible Euler equations, exterior domain, blow-up, impermeable boundary condition.
AB - <p style="text-align: justify;">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.</p>