TITLE: turbulence as an unsolved problem of classical mechanics
QUESTION [5 upvotes]: Why is it that turbulence is considered to be an unsolved problem of classical mechanics?  What is meant by "unsolved"?  Don't the Navier-Stokes equations apply to turbulent flows?  It's difficult to grasp these concepts because there doesn't seem to be a mathematically precise definition of turbulence.

REPLY [2 votes]: I think we don't need a mathematically precise definition of turbulence to make sense of "turbulence as an unsolved problem of classical mechanics".
The question of singularities in Navier-Stokes solutions is a challenging math problem but almost unrelated to "turbulence as an unsolved problem";
which in my opinion amounts to: what, if anything, is universal in the statistics of actual fluid flows at (extremely) high Reynolds numbers?
No answer yet, so unsolved seems right... (Well, no full answer: Kolmogorov's 4/5th law is a universal feature, but there should be more, for instance a probability measure on a space of velocity fields having suitable invariance properties with respect to Navier-Stokes or Euler dynamics).