Intermittency, cascades and thin sets in three-dimensional Navier-Stokes turbulence

How to handle 3D turbulent fluid flows theoretically and (more lately) computationally has been a problem that has been with us for more than a century. Two areas will be covered in this talk. Firstly, I will make a sketch of Kolmogorov’s 1941 theory and its more modern spin-offs. Secondly, I will summarize what is known about the regularity problem for the 3D Navier-Stokes equations which still stands as one of the great unsolved problems in modern applied mathematics. I will give particular attention to points where they touch.