The Exact General Solution of Painlev\'e's Sixth Equation (PVI) and The Exact General Solution of the Navier Stokes Equations with Applications to Boundary Layer Problems

TL;DR

This paper presents the first known exact general solutions for Painlevé's sixth equation, Navier-Stokes equations, and Prandtl boundary layer equations, offering new analytical tools for complex differential equations in physics.

Contribution

It introduces the first exact general solutions for PVI, Navier-Stokes, and boundary layer equations, advancing analytical methods in fluid dynamics and differential equations.

Findings

Exact solutions for Painlevé's sixth equation (PVI) provided.

Exact solutions for Navier-Stokes equations derived.

Exact solutions for Prandtl boundary layer equations obtained.

Abstract

This paper provides the first known exact general solutions of Painlev\'e's sixth equation (PVI) and the exact general solutions of the Navier Stokes equations and Prandtl's boundary layer equations.