The finite time blow-up for the Euler-Poisson equations in \Bbb Rⁿ

2008/03/12 by Dongho Chae, Chae, Dongho
Mathematics · #35B30 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B30 #msc:35Q35

paper · pdf · doi:10.48550/arxiv.0803.1788

11 pages

arxiv created 2008/03/12 · arxiv updated 2009/12/01

Abstract

We prove the finite time blow-up for C¹ solutions to the Euler-Poisson equations in \Bbb Rⁿ, n≥ 1, with/without background density for initial data satisfying suitable conditions. We also find a sufficient condition for the initial data such that C³ solution breaks down in finite time for the compressible Euler equations for polytropic gas flows.

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