Comment by tomjakubowski

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.

https://www.youtube.com/watch?v=4wEn9B7pDV4