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

Abstract

We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson equations in ${\mathbb{R}}^n$, $n\ge 1$, 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 pages

Cited by in corpus (2)

• Remarks on global existence of classical solution to multi-dimensional compressible Euler-Poisson equations with geometrical symmetry
• Large time WKB approximation for multi-dimensional semiclassical Schrödinger-Poisson system