  By introducing a new averaged quantity with a fast decay weight to perform
Sideris's argument (Commun Math Phys, 1985) developed for the Euler Equations,
we extend the formation of singularities of classical solution to the 3D Euler
Equations established in Sideris (1985) and Makino et al. (Jpn J Appl Math,
1986) for the initial data with compactly supported disturbances to the
spherically symmetric solution with general initial data in Sobolev space.
Moreover, we also prove the formation of singularities of the spherically
symmetric solutions to the 3D Euler-Poisson Equations, but remove the compact
support assumptions on the initial data in Makino and Perthame (Jpn J Appl
Math, 1990) and Perthame (Jpn J Appl Math, 1990). Our proof also simplifies
that of Lei et al. (Math Res Lett, 2013) for the Euler Equations and is
undifferentiated in dimensions.
