Existence of a forward self-similar stagnation flow of the Navier-Stokes equations

Abstract

In this paper we construct an exact forward self-similar solution, representing a stagnation flow, for the Navier-Stokes equations by solving a third order ordinary differential equations.

An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows with slips

“…Much attention has been paid so far and many excellent articles have been already published. We refer to [5], [6], [10] and [12] for instance and the references therein. Certain forms of exact solutions are reduced to the solvability of third-order ordinary differential equations (ODEs), whose types are similar to those coming from the Prandtl boundary layer theory.…”