What is needed to solve the Navier-Stokes equations' well-posedness problem?

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

http://www.claymath.org/millennium/
 
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matematikawan said:
I could win $1 million if I can solve this. :biggrin:

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?
 
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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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