  Motivated by the astrophysical problems of star formations from molecular
clouds, we make the first step on the possible behaviors of certain molecular
clouds. This article $(1)$ establishes the diffuse boundary problem of
Euler-Poisson system for describing the evolution of molecular clouds; $(2)$
proves the local existence, uniqueness and continuation principle of the
classical solution to the diffuse boundary problem; $(3)$ proves the classical
solution (without any symmetry condition) to the diffuse problem blows up at
finite time if there is no the first class of global solution and the data is
admissible (large scale, irregularly-shaped, expanding and rotational molecular
clouds); $(4)$ proves certain singularities can be removed from the boundary if
the data is strongly admissible. This result partially answers Makino's
conjecture $[69]$ on the finite blowup of any tame solution without symmetries
and gives the possibilities of star formations, fragmentation and possibilities
of formations of shocks and physical vacuum boundary in perfect fluids with
Newtonian self-gravity.
