  Presented are two results on the formation of finite time singularities of
solutions to the compressible Euler equations in two and three space dimensions
for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed
to be symmetric and the initial sound speed is required to vanish at the
origin. They are smooth in Sobolev space $H^3$, but not required to have a
compact support. It is shown that the $H^3$ norm of the velocity field and the
sound speed will blow up in a finite time.
