Unsolved problems in Maths & Fluid Mechanics/ CFD for the 21st century

Do the Navier–Stokes equations in R³ always have a unique smooth solution that extends for all time?

Proposed by Steve Smale in 1998, 1999.

Peter Constantin, Some open problems and research directions in the mathematical study of uid dynamics, http://www.people.cs.uchicago.edu/~const/2k.pdf