Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N

TL;DR

This paper constructs analytical blowup solutions for the N-dimensional pressureless Navier-Stokes-Poisson equations with density-dependent viscosity, extending previous solutions from Euler-Poisson equations in radial symmetry.

Contribution

It introduces new explicit blowup solutions for the pressureless Navier-Stokes-Poisson equations with density-dependent viscosity in multiple dimensions.

Findings

Constructed explicit blowup solutions in R^N

Extended solutions from Euler-Poisson to Navier-Stokes-Poisson equations

Demonstrated radial symmetry in solutions

Abstract

We study the N-dimensional pressureless Navier--Stokes-Poisson equations with density-dependent viscosity. With the extension of the blowup solutions for the Euler-Poisson equations, the analytical blowup solutions,in radial symmetry, in R^N are constructed.