Analytical solution of the incompressible Navier-Stokes equations

TL;DR

This paper presents an analytical solution to the incompressible Navier-Stokes equations using a power series method, providing detailed derivations and convergence analysis.

Contribution

It introduces a novel application of the power series method to derive an exact analytical solution for the incompressible Navier-Stokes equations.

Findings

Exact analytical solution derived

Method details and convergence discussed

Potential for solving complex fluid flow problems

Abstract

The Navier-Stokes equations, which govern fluid motions, are not resolved yet. This investigation relates to the application of the power series method to the incompressible Navier-Stokes equations. This method involves replacing variables by power series in the equations. The resulting relations allow the computation of the series coefficients from the initial and boundary conditions. All the steps of applying the method to the Navier-Stokes equations are detailed and the exact analytical solution is then established. The last part discusses the domain of convergence of the solution.