Note on "A. Gorguis, A reliable approach to the solution of Navier-Stokes equations, Appl. Math. Lett. 25 (2012) 2015-2017"

TL;DR

This paper critically examines Gorguis' claim of transforming Navier-Stokes equations into linear form via Cole-Hopf, clarifying that the cases are inherently linear and highlighting errors in the original work.

Contribution

It clarifies the limitations of Gorguis' approach, showing that the treated cases are inherently linear and correcting misconceptions about the transformation.

Findings

Gorguis' cases involve velocity potential governed by Laplace's equation.

External force must be conservative for the approach to hold.

Errors in the original Gorguis article are identified.

Abstract

Gorguis' claim of being able to transform Navier-Stokes equations into linear ones through the Cole-Hopf transformation is disputed. It is shown that the cases treated by Gorguis are intrinsically linear; involving a velocity potential (psi) that is governed by Laplace's equation. They require the external force to be conservative and the initial and boundary conditions to admit such cases of fluid flow. The pressure cannot be known a priori, as suggested by Gorguis, but is determined so that it can be consistent with (psi). Other errors in the cited article are also indicated.