Analytical Solutions to the Navier-Stokes-Poisson Equations with Density-dependent Viscosity and with Pressure

TL;DR

This paper derives analytical blowup solutions for the Navier-Stokes-Poisson equations considering density-dependent viscosity and pressure, extending previous solutions for related equations, and providing insights into their singularity formation.

Contribution

It introduces new analytical blowup solutions for the Navier-Stokes-Poisson equations with pressure and density-dependent viscosity, expanding the understanding of their solution behavior.

Findings

Constructed explicit blowup solutions with pressure

Extended previous solutions to include pressure effects

Provided analytical insights into solution singularities

Abstract

We study some particular solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure, in radial symmetry. With extension of the previous known blowup solutions for the Euler-Poisson equations / pressureless Navier-Stokes-Poisson with density-dependent viscosity, we constructed the corresponding analytical blowup solutions for the Navier-Stokes-Poisson Equations with density-dependent viscosity and with pressure.