Navier-Stokes Equations

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

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

Navier-Stokes Equations

I could win $1 million if I can solve this. http://www.claymath.org/millennium/  Quote by matematikawan I could win$1 million if I can solve this. http://www.claymath.org/millennium/
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?