# Analytic approach for homogeneous and non-homogeneous second order PDE's with an analytical solution of Navier Stokes Equations on $\mathbb{R}^3$ for a viscous incompressible fluid

## TL;DR

This paper introduces an analytic method to reduce second-order PDEs, including Navier-Stokes equations for viscous incompressible fluids, to first-order PDEs, simplifying the analysis of initial and boundary value problems.

## Contribution

The paper presents a novel analytic approach that simplifies second-order PDEs to first-order, facilitating easier proofs of existence and uniqueness for related problems.

## Key findings

- Reduction of second-order PDEs to first-order form
- Simplification of existence and uniqueness proofs
- Analytic solution for Navier-Stokes equations on ^3

## Abstract

Under this method second order \textbf{partial differential equations (PDE's)} can be reduce to first order PDE's, simplifying the Initial value problem \textbf{IVP} or Border value Problem \textbf{BVP} for most cases of second-order differential equation, letting easiest proofs for existence and uniqueness of the PVI and BVP problems.