TY - JOUR
A2 - Bohner, Martin
AU - Cheung, Ka Luen
AU - Wong, Sen
PY - 2016
DA - 2016/02/03
TI - Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry
SP - 3781760
VL - 2016
AB - 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)xα-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)+c˙(0)<0. As a corollary, the blowup properties of solutions with velocity of the form (a˙t/at)x+b(t)(x/x) are obtained. Our analysis includes both the isentropic case (γ>1) and the isothermal case (γ=1).
SN - 2356-6140
UR - https://doi.org/10.1155/2016/3781760
DO - 10.1155/2016/3781760
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -