The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156742We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson equations in $\Bbb R^n$, $n\geq 1$, with/without background density for initial data satisfying suitable conditions. We also find a sufficient condition for the initial data such that $C^3$ solution breaks down in finite time for the compressible Euler equations for polytropic gas flows.11 pagesAnalysis of PDEs35Q35, 35B30The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$text