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Title: New method for blowup of the Euler-poisson system
Authors: Kwong, MK
Yuen, M
Issue Date: 2016
Publisher: American Institute of Physics
Source: Journal of mathematical physics, 2016, v. 57, no. 8, 083501 How to cite?
Journal: Journal of mathematical physics 
Abstract: In this paper, we provide a new method for establishing the blowup of C2 solutionsfor the pressureless Euler-Poisson system with attractive forces for RN(N ≥ 2) with ρ(0, x0) > 0 and Ω0ij(x0) = 1/2[∂iuj(0, x0) - ∂jui(0, x0)]= 0 at somepoint x0 ∈ RN. By applying the generalized Hubble transformation div u(t, x0(t)) =Na˙(t )/a(t ) to a reduced Riccati differential inequality derived from the system, wesimplify the inequality into the Emden equation ä(t) = - Λ/a(t )N-1 , a(0) = 1, a˙(0) =div u(0, x0)/N . Known results on its blowup set allow us to easily obtain theblowup conditions of the Euler-Poisson system.
ISSN: 0022-2488 (print)
1089-7658 (online)
DOI: 10.1063/1.4960472
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