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We study the pressureless Navier--Stokes-Poisson equations of describing theevolution of the gaseous star in astrophysics. The isothermal blowup solutionsof Yuen, to the Euler-Poisson equations in R2, can be extended to thepressureless Navier-Stokes-Poisson equations with density-dependent viscosityin R3. Besides some remarks, about the meaning of the blowup solutions and theapplicability of such solutions to the the drift-diffusion model insemiconductors, are discussed in the end.

Analytical Blowup Solutions to the 3-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity