Analytical Collapsing Solutions to Pressureless Navier-Stokes-Poisson   Equations with Density-dependent Viscosity $\theta=1/2$ in $R^{2}$
  We study the 2-dimensional Navier-Stokes-Poisson equations with density-dependent viscosity $\theta=1/2$ without pressure of gaseous stars in astrophysics. The analytical solutions with collapsing in radial symmetry, are constructed in this paper. 
Manwai Yuen