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

TL;DR

This paper derives analytical collapsing solutions for the 2D pressureless Navier-Stokes-Poisson equations with density-dependent viscosity in radial symmetry, relevant to modeling gaseous stars in astrophysics.

Contribution

It provides the first explicit analytical solutions demonstrating collapse phenomena in the 2D pressureless Navier-Stokes-Poisson system with density-dependent viscosity.

Findings

Constructed explicit collapsing solutions in 2D

Demonstrated collapse behavior in radial symmetry

Applicable to astrophysical gaseous star models

Abstract

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.