Symmetry reduction and exact solutions of the Navier-Stokes equations

TL;DR

This paper introduces symmetry-based ansatzes that simplify the Navier-Stokes equations, leading to the derivation of numerous exact solutions across different variable dimensions.

Contribution

It presents new symmetry reduction techniques and constructs extensive sets of exact solutions for the Navier-Stokes equations.

Findings

Reduction of Navier-Stokes to simpler differential systems

Construction of large sets of exact solutions

Demonstration of symmetry methods in fluid dynamics

Abstract

Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed.