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http://hdl.handle.net/10397/62049
Title: | New method for blowup of the Euler-poisson system | Authors: | Kwong, MK Yuen, M |
Issue Date: | 2016 | Source: | Journal of mathematical physics, 2016, v. 57, no. 8, 83501, p. 083501-1-083501-5 | 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. | Publisher: | American Institute of Physics | Journal: | Journal of mathematical physics | ISSN: | 0022-2488 (print) 1089-7658 (online) |
DOI: | 10.1063/1.4960472 | Rights: | © 2016 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in M. K. Kwong and M. Yuen, J. Math. Phys. 57, 083501 (2016) and may be found at https://dx.doi.org/10.1063/1.4960472 |
Appears in Collections: | Journal/Magazine Article |
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