Navier-Stokes Equations

Winzer

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

MathematicalPhysicist

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

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

matematikawan

I could win $1 million if I can solve this.

http://www.claymath.org/millennium/

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?