Formation of Singularity for Compressible Euler Equations Outside a Ball in 3-D (Journal of Mathematical Study, 2024)
The initial boundary value problem for a compressible Euler system outside a ball in $R^3$ is considered in this paper. Assuming the initial data have small andcompact supported perturbations near a constant state, we show that the solution willblow 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 goodbehavior is introduced.
Keywords: Compressible Euler equations; exterior domain; blow-up; impermeable boundary condition.