New classes of exact solutions of three-dimensional Navier-Stokes equations

TL;DR

This paper introduces new classes of exact, physically interpretable solutions to the three-dimensional unsteady Navier-Stokes equations, including periodic solutions expressed with elementary functions, enhancing understanding of fluid dynamics.

Contribution

It presents novel classes of exact solutions with arbitrary functions and parameters, expanding the analytical solution space for the Navier-Stokes equations.

Findings

Derived various periodic solutions using elementary functions

Provided physical interpretation and classification of solutions

Expanded analytical solution methods for fluid dynamics

Abstract

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.