Rotationally Invariant and Partially Invariant Flows of a Viscous Incompressible Fluid and a Viscous Gas

Abstract

In this manuscript we study the Navier–Stokes equations and viscous gasdynamics equations. These equations play a central role in much of the research withinapplied mathematics, physics and engineering. One of the questions that we study here isthe existence of solutions of special vortex type for the Navier–Stokes equations and viscous gas dynamics equations. This type of solution for the inviscid gas and fluid dynamics equations was introduced by Ovsiannikov [1]. Note that this solution is partiallyinvariant with respect to group of rotations $O$(3). Another part of our study is devotedto the group classification of spherically symmetric viscous gas dynamics equations. Theapproach used is classical group analysis. We use the notions of invariant and partiallyinvariant solutions.