In this paper, we study the blowup of the N-dim Euler or Euler-Poisson equations with repulsive forces, in radial symmetry. We provide a novel integration method to show that the non-trivial classical solutions (ρ,V), with compact support in [0,R], where R>0
Nearby in the stack
is a positive constant and in the sense which
ρ(t,r)=0
and
V(t,r)=0
for
r≥R
, under the initial condition%
H0=∫0RrV0dr>0
blow up on or before the finite time
T=R3/(2H0)
for pressureless fluids or
γ>1.
The main contribution of this article provides the blowup results of the Euler
(δ=0)
or Euler-Poisson
(δ=1)
equations with repulsive forces, and with pressure
(γ>1)
, as the previous blowup papers (MUK MP, P and CT) cannot handle the systems with the pressure term, for