TY - JOUR
A2 - Khalique, C. M.
A2 - Baleanu, D.
AU - Wong, Sen
AU - Yuen, Manwai
PY - 2014
DA - 2014/03/30
TI - Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
SP - 580871
VL - 2014
AB - We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in RN. For time t≥0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P=Kργ, where ρ is the density function, K is a constant, and γ>1, we can show that the nontrivial C1 solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include rN-1ln(r+1), rN-1er, rN-1(r3-3r2+3r+ε), rN-1sin((π/2)(r/R)), and rN-1sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.
SN - 2356-6140
UR - https://doi.org/10.1155/2014/580871
DO - 10.1155/2014/580871
JF - The Scientific World Journal
PB - Hindawi Publishing Corporation
KW -
ER -