Blowups and longtime developments with near-boundary mass accretions of
  irregularly-shaped Euler--Poisson dominated molecular clouds in astrophysics
  Motivated by the astrophysical problems of star formations from molecular
clouds,we make the first step on the possible long time behaviors of certain
irregularly-shaped molecular clouds. We emphasis the main difficulty of the
blowups of the irregular-shaped fluids with vacuum (molecular clouds) comes
from the initial irregular configurations of its density (multiple centers of
gravity). This inevitably causes far more complicated movements during the
evolution than the one with spherical symmetry. The spherical symmetric case
has been well studied. However, for the non-spherical symmetric case with the
gravity, it is very rare in the references due to a very complicate nonlinear
interaction between the gravity and the fluids. This article concludes, under
the admissible data (i.e., large scale, irregularly-shaped, expanding and
rotational molecular clouds), the developments of the solution (molecular
clouds) are either global (the first class) with near-boundary mass accretions
(leads to star formations), or blowup at finite time. In addition, certain
singularities can be removed from the boundary if the data is strongly
admissible. This paper partially answers Makino's conjecture [37] in 1992 on
the finite time blowup of any tame solution without symmetries for some data
and the model of the molecular clouds and the local wellposedness have been
established in the companion article [30].
