Drifting Solutions with Elliptic Symmetry for the Compressible Navier-Stokes Equations with Density-dependent Viscosity

TL;DR

This paper derives a new class of drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity, generalizing previous solutions by Yuen using the characteristic method.

Contribution

It introduces a novel analytical solution class with elliptic symmetry for the Navier-Stokes equations with density-dependent viscosity, extending prior work by Yuen.

Findings

Derived drifting solutions with elliptic symmetry

Generalized Yuen's solutions using the characteristic method

Connected solutions to a generalized Emden dynamical system

Abstract

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen in [Yuen M.W. (2008), Analytical Solutions to the Navier-Stokes Equations, J. Math. Phys. 49, 113102], our solutions constitute a generalization of that obtained by Yuen.