Blowup phenomenon of solutions for the IBVP of the compressible euler equations in spherical symmetry

Ka Luen CHEUNG, Sen WONG

Research output: Contribution to journalArticles

Abstract

The blowup phenomenon of solutions is investigated for the initial-boundary value problem (IBVP) of the N-dimensional Euler equations with spherical symmetry. We first show that there are only trivial solutions when the velocity is of the form c(t)|x|∝⁻¹x+b(t)(x/|x|) for any value of α≠1 or any positive integer N≠1 . Then, we show that blowup phenomenon occurs when α = N = 1 and c²(0) + ć (0) < 0. As a corollary, the blowup properties of solutions with velocity of the form (à(t)/a(t))x + b(t)(x|x|) are obtained. Our analysis includes both the isentropic case (ƴ > 1) and the isothermal case (ƴ = 1) . Copyright © 2016 Ka Luen Cheung and Sen Wong.
Original languageEnglish
Article number3781760
JournalThe Scientific World Journal
Volume2016
DOIs
Publication statusPublished - Jan 2016

Citation

Cheung, K. L., & Wong, S. (2016). Blowup phenomenon of solutions for the IBVP of the compressible euler equations in spherical symmetry. The Scientific World Journal, 2016. Retrieved from http://dx.doi.org/10.1155/2016/3781760

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