The Newtonian Euler-Poisson equations with attractive forces are the classical models for the evolution of gaseous stars and galaxies in astrophysics .
In this paper , we use the integration method to study the blowup problem of the N -dimensional system with adiabatic exponent \gamma > 1 , in radial symmetry .
We could show that the C ^ { 1 } non-trivial classical solutions ( \rho,V ) , with compact support in [ 0 ,R ] , where R > 0 is a positive constant with \rho ( t,r ) = 0 and V ( t,r ) = 0 for r \geq R , under the initial condition

H _ { 0 } = \int _ { 0 } ^ { R } r ^ { n } V _ { 0 } dr > \sqrt { \frac { 2 R ^ { 2 n - N + 4 } M } { n ( n + 1 ) ( n - N + 2 ) } } with an arbitrary constant n > \max ( N - 2 , 0 ) , blow up before a finite time T for pressureless fluids or \gamma > 1. Our results could fill some gaps about the blowup phenomena to the classical C ^ { 1 } solutions of that attractive system with pressure under the first boundary condition . In addition , the corresponding result for the repulsive systems is also provided .
Here our result fully covers the previous case for n = 1 in ” M.W .
Yuen , Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces , Nonlinear Analysis Series A : Theory , Methods & Applications 74 ( 2011 ) , 1465–1470 ” .

2010 Mathematics Subject Classification : 35B30 , 35B44 , 35Q35 , 35Q85 , 85A05

Key Words : Euler-Poisson Equations , Integration Method , Blowup , Repulsive Forces , With Pressure , C ^ { 1 } Solutions , No-Slip Boundary Condition , Compact Support , Initial Value Problem , First Boundary Condition