# Navier-Stokes Equations

1. Jun 17, 2009

### Winzer

What does it take to look at the well poseness problem of the Navier stokes equations?
Besides knowledge in PDEs.

2. Jun 18, 2009

### MathematicalPhysicist

I guess that a good knowledge of fluid mechanics will be of great aid.

3. Jun 18, 2009

### Winzer

I'm sorry i should have clarified. I meant in the pure mathematical sense.
Prove or give a counter-example that:
In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations

4. Jun 18, 2009

I could win $1 million if I can solve this. http://www.claymath.org/millennium/ [Broken] Last edited by a moderator: May 4, 2017 5. Jun 18, 2009 ### Winzer Cool. It's agreed that if you solve this we'll split the$.

Anyway, what kind of insane math background does one need to attempt his journey?

Last edited by a moderator: May 4, 2017