Three dimensional compressible Navier-Stokes equation - self-similar and traveling wave solutions

Abstract

We investigate the three dimensional compressible Navier-Stokes and the continuity equations in Cartesian coordinates for Newtonian fluids. The polytropic equation of sate is used as closing condition. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz which was already used for non-compressible viscous flow in our former study (Commun. in Theor. Phys. 56, (2011) 745). In the second method the three dimensional traveling wave Ansatz was applied. The geometrical interpretations of the trial functions are also discussed.