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

TL;DR

This paper extends analytical solutions of the Navier-Stokes equations to include pressure effects with density-dependent viscosity, under specific restrictions on parameters, building upon previous pressureless solutions.

Contribution

It introduces new analytical solutions for the Navier-Stokes equations with pressure and density-dependent viscosity, expanding prior pressureless models.

Findings

Extended solution structure to include pressure

Applicable under specific parameter restrictions

Builds upon previous pressureless solutions

Abstract

This article is the continued version of the analytical solutions for the pressureless Navier-Stokes equations with density-dependent viscosity in "M.W. Yuen, Analyitcal Solutions to the Navier-Stokes Equations, J. Math. Phys., 49 (2008) No. 11, 113102, 10pp". We are able to extend the similar solutions structure to the case with pressure under some restriction for $\gamma$ and $\theta$.