The Navier-Stokes Equations

[Pro]

The Navier-Stokes Equations.

[Pro]

It's pretty much impossible for me to rewrite the protheory.com topics in full as I'd end up just making it too complicated so for now please just take a look at this original archive from my website and then you can ask me any questions below here

The Navier-Stokes Equations



Introduction

This problem is about the mathematical study of fluid flow.



Fluid

The word fluid refers to the characteristics of any flow able to be modelled.



Equations

The Navier-Stokes equations were formulated to predict and explain the hypothetical movements of fluids, and to examine the possibility for smoothness.



Model

The idea was to create a mathematical model that could describe and predict all "real life" flows in three dimensions.



Formula

The hope was that there may be a hidden method or formula that, when solved and properly understood, would unchangingly predict all possible characteristics of any fluid flow phenomena.



Variables

It was hoped that by considering variables such as time, mass, momentum, and energy balances, we could create an accurate and complete three dimensional fluid model.



Still

We still don't know whether these equations have a three dimensional solution or not, and even if such a solution does exist, the process of finding it has so far proved impossible.



Summary

Is there a three dimensional solution that can predict and explain all fluid flow phenomena?

Can a three dimensional solution to the Navier-Stokes equations be found?



The Millennium Problem

The Millennium problem is to make substantial progress towards a theory that can fully explain the Navier-Stokes Equations, and to prove whether or not they can be solved in three dimensions.

For the exact problem description please refer to Claymath.org



The Answer



Conjecture

The Navier-Stokes equations present us with two options, either the equations can be solved in three dimensions for all real life flows or they cannot, and asks us to choose one of them.



Fluid

An absolute and unchanging method or formula for predicting all possible fluid flow is a singular prediction and as such would be inaccurate.



Potentials

Even if we could ever manage to create some partially accurate model of fluid flow our predictions can never be unchangingly correct without considering the theoretical opposite and neutral potentials within all flows.



Dimensions

Three simultaneous dimensions require three simultaneous answers, just as two dimensions require two simultaneous answers.



Solved

This is why the equations have been solved in two dimensions but not in three.



Restricted

Two simultaneous dimensions restricts us to two opposites and three dimensions means that we are restricted to three simultaneous potentials.



Solution

1. There is a three dimensional solution within the Navier-Stokes equations.

2. There is not a three dimensional solution within the Navier-Stokes equations.

3. There is a neutral potential within the Navier-Stokes equations.

Simultaneously.



Am I wrong?

I simultaneously oppose, agree with, and neutralise all criticism ad infinitum.

My point is literal.

There is no point creating a theory of everything that doesn't work.