Analytical solutions to the Navier–Stokes equations with density-dependent viscosity and with pressure

Abstract

This article is the continued version of the analytical solutions for the pressureless Navier-Stokes equations with density-dependent viscosity [9]. We are able to extend the similar solutions structure to the case with pressure under some restriction to the constants γ and θ.

Some exact blowup or global solutions for the non-isentropic Navier–Stokes equations with density-dependent viscosity

“…h By comparing the previous isentropic cases [4], our main contribution in this brief article is to free the density function as an arbitrary positive C 1 function for the density-dependent Navier-Stokes system (2). The similar cases happen in the pressureless Euler and Navier-Stokes systems: [10,5,7].…”

“…It has never been seen in the previous literature for the systems with the pressure term (other than the pressureless Euler and Navier-Stokes equations without density-dependent viscosity) [2,8,9,4,6] by separation methods.…”

“…can be expressed by: [4] showed that there exists a family of the analytical solutions for the NavierStokes equations with density-dependent viscosity (8):…”

Analytical solutions to a class of non-Newtonian fluids with free boundaries

“…It is worthy mentioning that, L. H. Yeung and M. W. Yuen in Ref. 21, considered the Navier-Stokes equation…”

Analytical solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure

“…For the construction of analytical solutions to the Euler, Navier-Stokes and pressureless Navier-Stokes-Poisson equations, readers may refer to the recent results in [20], [19], [23] and [24].…”