Analytical Collapsing Solutions to Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity $θ=1/2$ in $R^{2}$

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We study the 2-dimensional Navier-Stokes-Poisson equations with density-dependent viscosity $θ=1/2$ without pressure of gaseous stars in astrophysics. The analytical solutions with collapsing in radial symmetry, are constructed in this paper.
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