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

TL;DR

This paper extends known blowup solutions from Euler-Poisson equations to pressureless Navier-Stokes-Poisson equations with density-dependent viscosity in three dimensions, relevant for astrophysics and semiconductor models.

Contribution

It introduces new analytical blowup solutions for 3D pressureless Navier-Stokes-Poisson equations with density-dependent viscosity, expanding the understanding of such models.

Findings

Existence of blowup solutions in 3D pressureless Navier-Stokes-Poisson equations.

Extension of 2D Euler-Poisson blowup solutions to 3D Navier-Stokes-Poisson.

Discussion on the physical implications and applications in astrophysics and semiconductors.

Abstract

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