Prove the existence of smooth solutions to a certain model

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You don't need to solve this, just tell me what problem it is... although if you do solve it you'll be a million dollars richer.

Prove the existence of smooth solutions to a certain model of incompressible fluid dynamics. This is the ... problem?
 
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It's the Navier-stokes problem and Clay Mathematics institute offers 1 million dollars prize to solve it or 6 other different problems (possibly 5 because the Poincare conjecture seems to have been solved recently)
 
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point for meteor!
 

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