Blowups and longtime developments with near-boundary mass accretions of irregularly-shaped Euler--Poisson dominated molecular clouds in astrophysics

Abstract

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].