New method for blowup of the Euler-Poisson system

Man Kam KWONG, Man Wai YUEN

Research output: Contribution to journalArticlespeer-review

4 Citations (Scopus)

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. Copyright © 2016 AIP Publishing.
Original languageEnglish
Article number083501
JournalJournal of Mathematical Physics
Volume57
Issue number8
Early online dateAug 2016
DOIs
Publication statusPublished - 2016

Citation

Kwong, M. K., & Yuen, M. (2016, August). New method for blowup of the Euler-Poisson system. Journal of Mathematical Physics, 57(8). Retrieved August 31, 2016, from http://dx.doi.org/10.1063/1.4960472

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