Article says that there are 2 formulations of the NS problem and both are interesting: one is about fluid behaviour with no external forces, other is about fluid behaviour with external forces.
For a counter-example the latter is easier since you can have a tricky external forcefield.
I learned from this charming lo-fi video that it is actually much easier to find singularities in the Navier-Stokes equation for compressible fluids (which is out of scope for the Millenium Prize problem). The first was found in 1998 by Zhouping Xin.
bmacho · · focus · HN ↗
For a counter-example the latter is easier since you can have a tricky external forcefield.
tomjakubowski · · focus · HN ↗
<a href="https://www.youtube.com/watch?v=4wEn9B7pDV4" rel="nofollow">https://www.youtube.com/watch?v=4wEn9B7pDV4